+0

0
252
8
+86

Cant figure this one out:

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

Oct 13, 2018

#1
-1

z=10 and i=12

Oct 13, 2018
#5
0

'i' is not a variable, it is a constant.

Guest Oct 14, 2018
#6
+102466
0

$$i=\sqrt{-1}$$

Melody  Oct 14, 2018
#3
+72
0

I answerd that, but why doesn't it count as me. I just registered

Oct 13, 2018
#4
+102466
0

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
+102466
+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
0

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

Guest Oct 14, 2018