What is ((sqrt(2))/2+(sqrt(2))/2 i)^4 ?

The solution to ((sqrt(2))/2+(sqrt(2))/2 i)^4 is -1

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simplify ((sqrt(2))/2+(sqrt(2))/2 i)^4

simplify

(\frac{2}{2} + \frac{2}{2} i)^{4}

- 1

Solution steps

(\frac{2}{2} + \frac{2}{2} i)^{4}

Simplify

\frac{2}{2} + \frac{2}{2} i : \frac{1}{2} + \frac{1}{2} i

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

Expand

(\frac{1}{2} + \frac{1}{2} i)^{4} : - 1

= - 1

4 x^{3} - 8 x^{2} - 9 x + 18

y^{2} + 50 y + 336

(3 x + 1) (2 x + 1)

\frac{x y}{x}

What is ((sqrt(2))/2+(sqrt(2))/2 i)^4 ?
The solution to ((sqrt(2))/2+(sqrt(2))/2 i)^4 is -1