Simplify $i^{19}$, $i^{30}$ and $i^{-672}$. Evaluate $i^{1+2+3+\dots+15}$. Simplify \(\left(

Question

Simplify $i^{19}$, $i^{30}$ and $i^{-672}$. Evaluate $i^{1+2+3+\dots+15}$. Simplify $\left(\frac{1+i}{1-i}\right)^{4n+2} + \left(\frac{1-i}{1+i}\right)^{4n+1}$, where $n$ is a positive integer.

Accepted Answer

(a) $-i,-1,1$ (b) $1$ (c) $-1-i$.

Powers of complex numbers

Powers of complex numbers

Solution:

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