Question

simplify (1+i)^8 (write in form a+bi)

Answer 1

easy

Answer 2

express 1+i in polar form

Answer 3

1+i = \[\sqrt{2}e ^{ \frac{i \pi}{4}}\]

Answer 4

then take the power

Answer 5

\[(1+I)^8 = [ \sqrt{2}e ^{\frac{i \pi}{4}}]^8\]

Answer 6

= \[(\sqrt{2})^8 e ^{8\frac{ i \pi} {4}}\]

Answer 7

= \[2^4 e ^{2 \pi i}\]

Answer 8

but \[ e^{2 \pi i } =1 \]

Answer 9

so answer = 2^4 = 16