We know that |ab|=|a| |b|. Therefore, |(1+i)^6|=|1+ i|^6Now, |1+i|=1^2+1^2=2Our answer is (2)^6=2^3=8.

jmc

algebra junior

Problem

Find

(1 + i)^{6}

Solution

We know that

∣ ab ∣ = ∣ a ∣ \cdot ∣ b ∣

. Therefore,

(1 + i)^{6} = ∣ 1 + i ∣^{6}

Now,

∣ 1 + i ∣ = 1^{2} + 1^{2} = 2

Our answer is

(2)^{6} = 2^{3} = 8

Final answer