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complex numbers

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41 items are filed under this topic.
Simplifying a complex expression 2021-12-15
From Grace:
Write in the form. a+bi, -6-7i+8i^2+4i3-5i^4
Answered by Penny Nom.
0^(a+bi) 2020-12-03
From Douglas:
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.)

Answered by Penny Nom.
Investigating y = (-2)^x 2020-01-13
From Gonzalo:
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.
Answered by Harley Weston.
Simplify 1/2^i 2018-01-28
From Deepak:
How do I simplify this complex equation:


Answered by Penny Nom.
x^2 = -16 2016-12-12
From A student:
x to the second power = -16

what number solves the equation?

Answered by Penny Nom.
The modulus of a complex number 2016-07-29
From Cheyenne:
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?

Answered by Penny Nom.
Complex numbers in standard form 2016-01-15
From Michael:
express the following complex numbers in standard form (2+3i)+(5-2i)
Answered by Penny Nom.
What is the value of |2((i)^(1/2))|? 2013-07-22
From Delilah:
What is the value of |2((i)^(1/2))| ?
i.e. absolute value of 2 multiplied by square root of i.

Answered by Penny Nom.
I started with Euler's identity and manipulated it 2011-11-14
From anonymous:
I started with Euler's identity and manipulated it
type it in in a calculator and you get e^pi=23.1406926... and (-1)^i=0.0432139183... What did I do wrong?

Answered by Robert Dawson.
Find all the roots 2010-12-02
From gagan:
find all the roots of z^5-3z^4+2z^3+z^2-3z+2
Answered by Stephen La Rocque and Penny Nom.
z^5 - 3z^4 + 2z^3 + z^2 - 3z + 2 2010-11-06
From Kumar:
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

Answered by Robert Dawson and Penny Nom.
A Squared Number That's Negative 2010-09-22
From David:
What is the only number that when it's squared becomes negative?
Answered by Stephen La Rocque.
Graphical Representation of Complex Numbers 2010-06-08
From Anas:
why do we write complex number a+ib as (a,b)?
Answered by Janice Cotcher.
(1-i)ln(1+i) 2008-05-02
From Kim:
I am stuck on the expansion of (1-i)ln(1+i)=(1-i)[ln(square root of 2)+i(3.14/4 = 2n3.14)]
Answered by Harley Weston.
Imaginary roots 2007-12-09
From Josh:
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)?
Answered by Harley Weston.
Complex numbers 2007-10-27
From Dylan:
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?

Answered by Penny Nom.
(1 - i)^5 2007-07-24
From sofia:
Compute the given arithmetic expression and give the answer in the form a + bi where a,b element in R. 1. (1 - i)^5
Answered by Harley Weston.
A complex number in polar form 2007-07-23
From roland:
write the given complex number z in polar form lzl(p+qi) where lp + qil=1 for 3 - 4i.
Answered by Harley Weston.
Simplifying complex denominators 2007-06-21
From Krys:
How do I simplify completely? ((4+i ) / (3+i )) - ((2-i ) / (5-i ))
Answered by Stephen La Rocque.
-12/(7 - i) 2007-04-18
From Diana:
Perform the operation. Write all answers in a + bi form.

7 - radical -1

Answered by Penny Nom.
Using complex numbers 2007-03-12
From Kara:
Do you use complex numbers in your job?
Answered by Stephen La Rocque and Penny Nom.
Exponential form of complex numbers 2007-02-12
From Austin:
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
Answered by Penny Nom.
The absolute value of imaginary and complex numbers 2006-12-11
From Keith:
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


Answered by Stephen La Rocque and Penny Nom.
how do i find i^22? 2006-06-12
From Sky:
how do i find i22?

Answered by Stephen La Rocque.
sinh(i/2) 2006-02-09
From Louis:
How can you set up an equation to find sinh(i/2)
Answered by Penny Nom.
The square root of i 2005-11-30
From Kevin:

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?

Answered by Claude Tardif.
z^2 = 3 - 4i 2004-03-26
From John:
Solve: Z^2 = 3 - 4i
Answered by Harley Weston.
Real numbers 2003-05-09
From Sirena:
what is a "real" number
Answered by Penny Nom.
a+b=10 and ab=40 2002-04-27
From April:
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.

Answered by Penny Nom.
The square root of i 2002-03-14
From Arlene:
what is the square root of i, if i=x+yi?

what is the square root of 1-i? i'm getting problems like these in which I do not understand.

Answered by Harley Weston.
eix = cosx + isinx 2001-10-10
From Peter:
Given: eix = cosx + isinx
  1. substitute -x for x to find e-ix, simplifying your answer

  2. use the given and part a to find an identity for cosx making no reference to trig functions

  3. find an identity for sinx
  4. .
  5. .

Answered by Penny Nom.
Powers of i 2000-05-24
From Paul Fieldhouse :
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?
Answered by Penny Nom.
The square root of -1 2000-05-19
From Gary:
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
Answered by Harley Weston.
root(-1)* root(-1) 2000-03-20
From Michael Moran:
i squared = -1


i squared = root(-1)* root(-1)
= root( -1*-1)
= root(1)
= 1
-1 doesn't = 1

can you help me with my question

Answered by Claude Tardif.
Complex numbers/polar coordinates 1999-03-25
From Kate Cegelis:
What is the relationship between complex numbers and polar coordinates?
Answered by Harley Weston.
Absolute value of i 1999-01-06
From Wayne Bagley:
I would like to know what is the absolute value of i. I need an answer suitable for the secondary level.
Answered by Harley Weston.
Complex numbers and the quadratic formula 1998-12-25
From Richard Peter:
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)

3x2+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?
Answered by Harley Weston.

Complex Numbers 1998-12-23
From Wayne Bagley:
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.
Answered by Harley Weston.
Two Problems 1998-07-28
From James Pulver:
How do you solve these problem? If log abc=16 and log ac=12 , find b. (The logs are log base 10.)
If a and b are real numbers, i^2 = -1 and (a+b)+5i=9+ai what is the value of b?

Answered by Jack LeSage.
Multiplying imaginary numbers. 1997-11-03
From Jim Catton:
Here is the question:

(square root -2) x (square root -8)

My algebra suggests two possibilities .

Answered by Walter Whiteley, Chris Fisfer and Harley Weston.

Complex numbers 1995-10-22
From Jacquie:
Why should we teach complex numbers in high school?
Answered by Harley Weston.



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