Use binomial theorem to find the complex number

[chwala]

Homework Statement

If $z=a+bi$, where $a$ and $b$ are real, use binomial theorem to find the real and imaginary parts of $z^5$

Relevant Equations

Complex numbers

This is also pretty easy,
$$
$$
$$
$$
$$

Any other variation, combinations may also work...

 

[PeroK]

$(a+bi)^5= a^5+\dfrac {5a^4bi}{1!}-\dfrac {20a^3(bi)^2}{2!}-\dfrac {60a^2(bi)^3}{3!}+\dfrac {120a(bi)^4}{4!}+\dfrac {120(bi)^5}{5!}$

You should have $$ throughout that equation. That said, you got the right answer.

 

[chwala]

You should have $+$ throughout that equation. That said, you got the right answer.

True, let me amend that...