Author Topic: convert these complex numbers from polar form to coordinate form (Read 738 times) Tweet Share

M-D · « **on:** May 11, 2013, 08:58:00 pm »

hi,

I've got these 3 complex numbers in polar form and the answers are in coordinate form. I am having difficulty converting them to coordinate form. here are the numbers:

1) $\frac{\sqrt{2}}{2^5}e^{-i3pi/4}$

the answers say: - $\frac{1}{32}(1+i)$

2) $2^7\sqrt{2}$ e^{ipi/4}[/tex]

the answers say: $128(1+i)$

3) $2^6e^{-i5pi}$

the answers say: $-64$

your help is greatly appreciated

b^3 · « **Reply #1 on:** May 11, 2013, 09:12:01 pm »

Hint: $e^{i \theta}=\cos(\theta)+ i \sin(\theta)$

Spoiler

e.g
$\begin{aligned}\frac{\sqrt{2}}{2^{5}}e^{-\frac{3\pi i}{4}} & =\frac{\sqrt{2}}{2^{5}}\left(\cos\left(-\frac{3\pi}{4}\right)+i\sin\left(-\frac{3\pi}{4}\right)\right) \\ & =\frac{\sqrt{2}}{2^{5}}\left(-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right) \\ & =\frac{\sqrt{2}\times-\sqrt{2}}{2^{5}\times2}\left(1+i\right) \\ & =\frac{-2}{2^{6}}\left(1+i\right) \\ & =-\frac{1}{32}\left(1+i\right) \end{aligned} $

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Author Topic: convert these complex numbers from polar form to coordinate form (Read 738 times) Tweet Share

M-D

convert these complex numbers from polar form to coordinate form

b^3

Re: convert these complex numbers from polar form to coordinate form

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