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Cant figure this one out:

Suppose \(z\)  is a complex number such that \(z^3 = 100+75i\) . Find \(|z|\).

 Oct 13, 2018
 #1
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-1

z=10 and i=12

 Oct 13, 2018
 #5
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'i' is not a variable, it is a constant.

Guest Oct 14, 2018
 #6
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\(i=\sqrt{-1}\)

Melody  Oct 14, 2018
 #3
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I answerd that, but why doesn't it count as me. I just registered

 Oct 13, 2018
 #4
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I did not give you the minus but without any explanation your answer has absolutely no value.

Someone else was expressing that when they gave you a minus point.

Melody  Oct 14, 2018
 #7
avatar+100256 
+2

Suppose z  is a complex number such that \(z^3 = 100+75i\) . Find |z|

 

\(|z^3| = \sqrt{100^2+75^2}\\ |z^3| = \sqrt{100^2+75^2}\\ |z^3| = 125\\ z^3=125[\frac{100+75i}{125}]\\ z^3=125[\ 0.8+0.5i]\\ \)

 

Let

\(z=re^{i\theta}\\ z^3=r^3e^{3i\theta}\\ z^3=r^3(cos(3\theta) +isin(3\theta))\\ \)
\(r^3(cos(3\theta) +isin(3\theta))=125[\  0.8+0.6i]\\ r^3=125\\ r=5\\ cos(3\theta)=0.8\\ sin(3\theta)=0.6\\ 3\theta \approx 0.6435\\ \theta \approx 0.2145\;radians\\ \)

 

anyway, I digress,

 

\(|z|=5\)

 

 

 

 

 


 

 Oct 14, 2018
 #8
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0

When z3=a there are 3 possible values for z not 1 (unless a=0)

Guest Oct 14, 2018

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