We know that |ab|=|a| |b|. Therefore, |( 35+ 45 i)^6|=| 35+ 45 i|^6Now, | 35+ 45i|=( 35)^2+( 45)^2=1Our answer is 1^6=1.

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jmc

algebra junior

Problem

Find

(\frac{3}{5} + \frac{4}{5} i)^{6}

Solution

We know that

∣ ab ∣ = ∣ a ∣ \cdot ∣ b ∣

. Therefore,

(\frac{3}{5} + \frac{4}{5} i)^{6} = \frac{3}{5} + \frac{4}{5} i^{6}

Now,

\frac{3}{5} + \frac{4}{5} i = (\frac{3}{5})^{2} + (\frac{4}{5})^{2} = 1

Our answer is

1^{6} = 1

Final answer