# Chapter 1 - Section 1.6 - Complex Numbers - 1.6 Exercises - Page 64: 49

$(3i)^{5}=243i$

#### Work Step by Step

$(3i)^{5}=3i\times3i\times3i\times3i\times3i=3^{5}\times i^{5}=243\times\sqrt -1$ because $i^{5}=\sqrt -1=i$ . Hence $243\times i=243i$ Hence the answer written in the form $a+bi$ where $a$ represents the real part and $b$ represents the imaginary part is $243i$ because $a=0$ and $b=243$ hence there is no real part only imaginary.

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