(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the following in x+iy form.

i^{3+i}

2. Relevant equations

i=re^{i[itex]\Theta[/itex]}

3. The attempt at a solution

i=re^{i[itex]\frac{pi}{2}[/itex]}

i^{3+i}= i^{3}*i^{i}

(-i)(e^{i2[itex]\frac{pi}{2}[/itex]})

=-ie^{-[itex]\frac{pi}{2}[/itex]}

=-.2079i

I understand how it all works out except [itex]\frac{pi}{2}[/itex]. I can't figure out how they got [itex]\frac{pi}{2}[/itex] in the first place. Any ideas? Thanks in advance.

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# Engineering Math - Complex Roots and Powers

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