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Algebra Level 3

What is $(CiSθ)^{100}$ if $θ= \frac{ \pi}{2}$ ?

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2 solutions

Sharky Kesa
Apr 1, 2015

I do believe you mean $(cis \theta)^{100}$

$\begin{aligned} (cis \theta)^{100} & = (e^{i \theta})^{100}\\ & = (e^{i \frac{pi}{2}})^{100}\\ & = e^{50i \pi}\\ & = (-1)^50\\ & = 1 \end{aligned}$

Yeah , I did mean that $CiS \theta = \cos \theta + i\sin \theta$

A Former Brilliant Member - 6 years, 2 months ago

Mehul Arora
Dec 26, 2014

Bro, There is a typo here so i suggest you correct it @Azhaghu Roopesh M

The question should say

"What is COS Theta if Theta = 0 degrees"

Now, As for the solution, I think there is no need ;)

Cheers!!