# Chapter 1 - Section 1.6 - Complex Numbers - 1.6 Exercises: 48

$i^{10}=-1$

#### Work Step by Step

$i^{10}=(i^{2})^{5}$ and $i^{2}=\sqrt -1\times\sqrt -1=-1$ hence $i^{10}=(-1)^{5}$. $(-1)^{5}=-1\times-1\times-1\times-1\times-1=-1$. Hence the asnwer written in the form $a+bi$ where $a$ represents the real part and $b$ represents the imaginary part is $-1$ because $a=-1$ and $b=0$ as there is no imaginary part.

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