







Simplifying a complex expression 
20211215 

Grace pose la question : Write in the form. a+bi,
67i+8i^2+4i35i^4 Penny Nom lui répond. 





0^(a+bi) 
20201203 

Douglas pose la question : I realize raising 0^a = 0 if a>0 and undefined if a<=0.
If have read that 0^bi is undefined for all b.
What I don't understand is why 0^(a+bi) = 0 if a and b are not equal to zero.
Is this purely by definition or is there a logical reason why this is the case?
(I have taken Complex Analysis, so have a fairly good understanding of complex numbers.) Penny Nom lui répond. 





Investigating y = (2)^x 
20200113 

Gonzalo pose la question : This is not precisely a maths question, but it is formulated based on my maths curiosity. Fidgetting with my new graphic calculator, I started graphing things and had the idea to graph $y=(2)^x.$
The result surprised me, and I thought a little bit about it, stored it on the back of my brain, and promised myself to look deeper into it someday. Harley Weston lui répond. 





Simplify 1/2^i 
20180128 

Deepak pose la question : How do I simplify this complex equation:
z=1/(2^i) Penny Nom lui répond. 





x^2 = 16 
20161212 

A student pose la question : x to the second power = 16
what number solves the equation? Penny Nom lui répond. 





The modulus of a complex number 
20160729 

Cheyenne pose la question : There's a question on my Summer Assignment I cant figure out. Here it is:
Find the absolute Value of the complex number. 5i
Please help? Penny Nom lui répond. 





Complex numbers in standard form 
20160115 

Michael pose la question : express the following complex numbers in standard form (2+3i)+(52i) Penny Nom lui répond. 





What is the value of 2((i)^(1/2))? 
20130722 

Delilah pose la question : What is the value of 2((i)^(1/2)) ?
i.e. absolute value of 2 multiplied by square root of i. Penny Nom lui répond. 





I started with Euler's identity and manipulated it 
20111114 

anonymous pose la question : I started with Euler's identity and manipulated it
e^i*pi=1
e^i*pi=(1)^1
e^i*pi=1
e^i*i*pi=(1)^i
e^pi=(1)^i
e^pi=(1)^i
type it in in a calculator and you get e^pi=23.1406926... and
(1)^i=0.0432139183... What did I do wrong? Robert Dawson lui répond. 





The square root of z=3+4i 
20111027 

dianah pose la question : how to find the square roots of complex number, z=3+4i Robert Dawson lui répond. 





Find all the roots 
20101202 

gagan pose la question : find all the roots of z^53z^4+2z^3+z^23z+2 Stephen La Rocque and Penny Nom lui répond. 





z^5  3z^4 + 2z^3 + z^2  3z + 2 
20101106 

Kumar pose la question : would you please solve this problem, related to complex numbers.
Find all the roots of :
z^5  3z^4 + 2z^3 + z^2  3z + 2 Robert Dawson and Penny Nom lui répond. 





A Squared Number That's Negative 
20100922 

David pose la question : What is the only number that when it's squared becomes negative? Stephen La Rocque lui répond. 





Graphical Representation of Complex Numbers 
20100608 

Anas pose la question : why do we write complex number a+ib as (a,b)? Janice Cotcher lui répond. 





Complex roots 
20100414 

Lan pose la question : If b and c are real numbers so that the polynomial (x^2) + bx + c has 1 + i as a zero, find b + c. Penny Nom lui répond. 





Zeros of a polynomial 
20100301 

Gavin pose la question : Suppose the polynomial R(x) = a_9x^9+a_8x^8+...+a_1x+a_0 has real coefficients with a_9≠0. Suppose also that R(x) has the following zeros:
2,
3,
i
Using this info, answer the following.
a. What is another zero of R(x)?
b. At most how many real zeros of R(x) are there?
c. At most how many imaginary zeros of R(x) are there?
p.s. I used _ for subscript
thanks so much Harley Weston lui répond. 





A quadratic equation with roots (4i) and (4+i) 
20090505 

Kelly pose la question : find a quadratic equation with roots (4i) and (4+i) Harley Weston lui répond. 





Find a polynomial function with the indicated zeros and satisfying the given conditions 
20090323 

Kristen pose la question : Find a polynomial function with the indicated zeros and satisfying the given conditions. Simplofy your answer (no imaginary numbers or parentheses in the answer)
Zeros: 1+2i, 12i, 5 ; f(2)=1 Harley Weston lui répond. 





What is i^i? 
20081227 

randomness pose la question : i have learnt that 'i' is square root of 1. What is then i^i ? It baffles my maths teacher... Robert Dawson and Penny Nom lui répond. 





Factor 9x^2 + 6x + 4 
20081121 

Jonah pose la question : how can i solve this by factoring: 9x^2 + 6x + 4 Harley Weston lui répond. 





A quadratic equation 
20080603 

Drew pose la question : A solution of x^28x=17 is
4 or 4+I or 4 or 4+i Janice Cotcher lui répond. 





(1i)ln(1+i) 
20080502 

Kim pose la question : I am stuck on the expansion of (1i)ln(1+i)=(1i)[ln(square root of 2)+i(3.14/4 = 2n3.14)] Harley Weston lui répond. 





Find the quadratic equation with roots at (3i) and its complex conjugate 
20080422 

Tiffany pose la question : Find the quadratic equation with roots at (3i) and its complex conjugate. Penny Nom lui répond. 





A complex cubic polynomial 
20080326 

wael pose la question : how do we solve in C the following equation:
z^3 + (5i6)z^2 + (924i)z + 13i + 18 = 0 if it admits a pure imaginary root? Harley Weston lui répond. 





A complex quadratic 
20080218 

Ash pose la question : z^2(6+2i)z+(8+6i)=0
Solve for Z Steve La Rocque and Penny Nom lui répond. 





Imaginary roots 
20071209 

Josh pose la question : What is the correlation between imaginary roots (of a quadratic or other
polynomial equation) and the graph of the equation? As in, how can one
represent imaginary solutions graphically (and why does that work)? Harley Weston lui répond. 





Complex numbers 
20071027 

Dylan pose la question : My problem is to prove:
z^2 = zz* Where z is the complex number x + iy and z* is it's complex conjugate x  iy.
If the absolute value of i is 1, then it looks like: z^2 = x+y x+y = x^2 + 2xy + y^2
And zz* = x^2 + y^2. for these to be equal, 2xy = 0. This seems wrong to me. What am I doing wrong? Penny Nom lui répond. 





(1  i)^5 
20070724 

sofia pose la question : Compute the given arithmetic expression and give the answer in the form a + bi where a,b element in R.
1. (1  i)^5 Harley Weston lui répond. 





A complex number in polar form 
20070723 

roland pose la question : write the given complex number z in polar form lzl(p+qi) where lp + qil=1 for 3  4i. Harley Weston lui répond. 





Simplifying complex denominators 
20070621 

Krys pose la question : How do I simplify completely?
((4+i ) / (3+i ))  ((2i ) / (5i )) Stephen La Rocque lui répond. 





(1+i)^(2i) 
20070426 

Eilis pose la question : How do I solve (1+i) to the power of 2i?
i.e. (1+i)^(2i) Penny Nom lui répond. 





12/(7  i) 
20070418 

Diana pose la question : Perform the operation. Write all answers in a + bi form.
12

7  radical 1 Penny Nom lui répond. 





Using complex numbers 
20070312 

Kara pose la question : Do you use complex numbers in your job? Stephen La Rocque and Penny Nom lui répond. 





Exponential form of complex numbers 
20070212 

Austin pose la question : When dealing with imaginary numbers in engineering, I am having trouble getting things into the exponential form. The equation is 1+i now I do know that re^(theta)i = r*cos(theta) + r*i*sin(theta). Just not quite understanding the order of operations. Thanks Penny Nom lui répond. 





The absolute value of imaginary and complex numbers 
20061211 

Keith pose la question : i don't get how to find the absolute value of imaginary and complex numbers here is an examples from the text book the answers are given but they don't show the work so i can follow along just show me the work please and explain how it is done
problem 3+4i Stephen La Rocque and Penny Nom lui répond. 





Is this unsolvable? 
20060919 

Al pose la question : Is this unsolvable???
2xy + 3x^2  3y + y^3 = 4x + 3 where y=3. Penny Nom and Claude Tardif lui répond. 





how do i find i^22? 
20060612 

Sky pose la question : how do i find i^{22}?
Sky Stephen La Rocque lui répond. 





sinh(i/2) 
20060209 

Louis pose la question : How can you set up an equation to find sinh(i/2) Penny Nom lui répond. 





The square root of i 
20051130 

Kevin pose la question :
If the square root of 1 is i, what is the square root of i?
How can you find the log of a negative number?
What is the log of 1?
Claude Tardif lui répond. 





A graph with certain properties 
20041122 

A student pose la question : i was asked as a question in coursework to sketch the graph with the following characteristics:
a double root at 3
a pair of imaginary roots
an xintercept at 6
a root at 4 which is not a double root Penny Nom lui répond. 





Imaginary roots of a ploynomial 
20041031 

Jennifer pose la question : how to find the roots of a polynomial equation if it would be imaginary? Harley Weston lui répond. 





(a+b) + 5i = 9 + ai 
20040625 

Josh pose la question : The question which someone gave you (a+b) + 5i = 9 + ai question) gave me trouble. Penny Nom lui répond. 





3+4i abd 3+4i 
20040617 

Sandy pose la question : how would you do a question like 3+4i? is that different than just doing 3+4i? Penny Nom lui répond. 





z^2 = 3  4i 
20040326 

John pose la question : Solve: Z^2 = 3  4i Harley Weston lui répond. 





A new way to measure randomness 
20031231 

Stephanie pose la question :
Last year, I did a science project in which I asked, "Which shuffles better, an automatic card shuffler or shuffling by hand?" To measure this I decided the "best" shuffler was the one to become random first. Last year, to measure randomness, I numbered cards 152 and had the subjects shuffle them until they broke up the rising sequences or reached 10 shuffles. (Usually 10 shuffles came first...) Anyway, I did the same thing with the automatic card shuffler, and, as hypothesized, the automatic card shuffler randomized the deck first.
This year, I have decided to continue the project. The problem is, I need a new way to measure randomness without the use of fancy computers or something. I have searched the Internet, I have posted my query on websites based on math, and I have searched the local library.
I have found many useful things on the Internet, but none of them can tell me a new way to measure randomness. I cannot do a perfect shuffle, and I am not terribly gifted in the art of using computers. If you have any information (anything will help) or advice, I would be greatly obliged. Andrei Volodin lui répond. 





A triangle in the complex plane 
20030710 

Scott pose la question : The vertices O and A of an EQUILATERAL triangle OAB in the complex plane are located at the origin and 3 + 3i. Find all possible values for the complex number representing the vertex B. Give the location of B in both polar and cartesian form (to 2.d.p) Penny Nom lui répond. 





Real numbers 
20030509 

Sirena pose la question : what is a "real" number Penny Nom lui répond. 





A complex quadratic 
20021006 

Michael pose la question : I would like to know, how to solve this Complex number: quadratic equation. ix^{ 2} + x i = 0 Harley Weston lui répond. 





a+b=10 and ab=40 
20020427 

April pose la question : What two numbers add to ten and multiply to forty? (a+b=10, a*b=40) I think the answer includes radicals and/or imaginary numbers. Penny Nom lui répond. 





The square root of i 
20020314 

Arlene pose la question : what is the square root of i, if i=x+yi? what is the square root of 1i? i'm getting problems like these in which I do not understand. Harley Weston lui répond. 





e^{ix} = cosx + isinx 
20011010 

Peter pose la question : Given: e^{ix} = cosx + isinx  substitute x for x to find e^{ix}, simplifying your answer
 use the given and part a to find an identity for cosx making no reference to trig functions
 find an identity for sinx
 .
 .
Penny Nom lui répond. 





Some complex problems 
20010115 

Nick pose la question : I am having enormous difficulty with one question in my maths homework. The question is shown below. If anybody out there can find the answers and show the workings and help me to understand. Harley Weston lui répond. 





A complex calculation 
20001124 

Angie pose la question : Multiply (32i)^{2}=3^{2}2(3)(2i)+(2i)^{2} Penny Nom lui répond. 





The magnitude of a complex number 
20001111 

Jeremy pose la question : Recently, we started studying how to graph complex numbers. Our math teacher said to use what would normally be the xaxis as the realaxis and to use the yaxis as the imaginaryaxis. However, when he started talking about how to calculate magnitude, that's when I became confused. For instance... Walter Whiteley lui répond. 





Powers of i 
20000524 

Paul Fieldhouse pose la question : What is the result of raising i to the googol power? is there a rule or pattern to raising i by increasing powers of 10? Penny Nom lui répond. 





The square root of 1 
20000519 

Gary pose la question : i am not a student i am just some one that heard something and i can't be sure on the answer...my ? is what is the square root of 1? i think it is 1 but not sure can you let me know please thank you Harley Weston lui répond. 





root(1)* root(1) 
20000320 

Michael Moran pose la question : i squared = 1 but i squared = root(1)* root(1) = root( 1*1) = root(1) = 1 1 doesn't = 1 can you help me with my question Claude Tardif lui répond. 





Complex Roots 
20000124 

Jess Rutherford pose la question : How do I find the value of k when 5x^{2} + k = 3x and has complex roots ? Penny Nom lui répond. 





Complex numbers/polar coordinates 
19990325 

Kate Cegelis pose la question : What is the relationship between complex numbers and polar coordinates? Harley Weston lui répond. 





Absolute value of i 
19990106 

Wayne Bagley pose la question : I would like to know what is the absolute value of i. I need an answer suitable for the secondary level. Harley Weston lui répond. 





Complex numbers and the quadratic formula 
19981225 

Richard Peter pose la question : My age is 16, and my name is Richard. My question relates to the topic complex numbers & the quadratic formula. I would like to know how to solve quadratic equations in which the discriminant is less than 0 (i.e. we get two complex solutions to the quadratic) 3x^{2}+2x+5 = 0 and how mathematicians like euler contributed to this field. If it would be possible I would also like to know how this type of quadratic equations can be graphed? Harley Weston lui répond. 





Complex Numbers 
19981223 

Wayne Bagley pose la question : I would like to know what is the square root of i , and i squared? I am looking for a response appropriate for secondary level students. Harley Weston lui répond. 





Two Problems 
19980728 

James Pulver pose la question : How do you solve these problem? If log abc=16 and log ac=12 , find b. (The logs are log base 10.) and If a and b are real numbers, i^2 = 1 and (a+b)+5i=9+ai what is the value of b? Jack LeSage lui répond. 





Multiplying imaginary numbers. 
19971103 

Jim Catton pose la question : Here is the question: (square root 2) x (square root 8) My algebra suggests two possibilities . . .
Walter Whiteley, Chris Fisfer and Harley Weston lui répond. 





How do you raise a number to an imaginary/complex power? 
19960703 

Andy Golden pose la question : How do you raise a number to an imaginary/complex power? I know how you raise "e" to a complex power, like e^(pi*i): cos pi + i * sin pi But what about numbers other than "e"? What if I want to raise 5 to the 2i power? How is that done? Chris Fisher lui répond. 





Complex numbers 
19951022 

Jacquie pose la question : Why should we teach complex numbers in high school? Harley Weston lui répond. 

