Question

4th root of: (10e^(iπ/2))
CALCULATE and GIVE YOUR ANSWER in CARTESIAN FORM!

Answer 1

\[(10e^{i \pi/2})^{1/4} = \sqrt[4]{10} e^{i \pi/8} = \sqrt[4]{10}(\cos \frac{\pi}{8} +i \sin \frac{\pi}{8})\]

Answer 2

do you need all 4 roots?

Answer 3

well i need a final answer

Answer 4

so i guess yes. because i need any info to write in Cartesian form

Answer 5

cartesian form is just a+bi
a = rcos
b = rsin

Answer 6

ok so then how would i write my final answer

Answer 7

\[r(\cos \theta +i \sin \theta) ^{1/4} = r^{1/4} (\cos \frac{\theta +2\pi k}{4} +i \sin \frac{\theta +2\pi k}{4})\]
k = 0,1,2,3
this gives 4 solutions
in cartesian form:
\[\sqrt[4]{10} \cos \frac{\pi/2 +2\pi k}{4} +\sqrt[4]{10}\sin \frac{\pi/2 +2\pi k}{4} i\]

Answer 8

thanks for your help

Answer 9

your welcome

here is calculator to verify
http://www.wolframalpha.com/input/?i=%2810e%5E%28i+pi%2F2%29%29%5E1%2F4