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November 10th, 2012, 06:57 PM   #1
Ter
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complex conjugates

Hi, I've a question about complex numbers in polar form. If z= 5cis(40), then will -z be -5cis(40)or -5cis(-40)? Thank you!
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November 10th, 2012, 08:16 PM   #2
jks
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Re: complex conjugates

I'm not sure if you are asking about taking the complex conjugate or performing negation. Your title is 'complex conjugates' but your symbolism is negation.

Also, a number in polar form such as 5cis(40) never has a negative magnitude (the 5 in this case). This is because the magnitude is the (positive) square root of the sum of the squares of the real and imaginary parts. The angle takes care of the signs as seen below.

First, some symbol clarification. If z is a complex number then the negative of z is denoted by -z. The complex conjugate is denoted by z*.

So let's use your example of z = 5cis(40) = 3.830 + 3.214i

The complex conjugate is z* = 5cis(-40) = 3.830 - 3.214i (the imaginary term is negated, so therefore the angle is negated)

The negative of z is -z = 5cis(40+180) = 5cis(40-180) = -3.830 - 3.214i (both real and imaginary terms are negated, so therefore the angle is increased or decreased by 180 degrees)
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