I was just wondering if the rules of exponents still applied to imaginary and complex numbers, like if $(2^4)^i=2^{4i}$ or not and if $(4^i)^i=4^{-1}$, etc
Can I raise a number to the power of i?
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complex-analysis
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0Short version: Yes, but you have to be careful. – 2012-09-15
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2If you write the complex number in polar form $z=re^{i\theta}$ you can see that $(re^{i\theta})^i=re^{i^2\theta}=re^{-\theta}$. – 2012-09-15
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1Why is $r$ not raised to the $i$ in these comments? – 2012-09-15