- #1

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## Homework Statement

Simplify [itex](1+i\sqrt{2})^5-(1-i\sqrt{2})^5[/itex]

## Homework Equations

[tex]z=a+bi[/tex]

[tex]z=r(cos\varphi+isin\varphi)[/tex]

[tex]tg\varphi=\frac{b}{a}[/tex]

[tex]r=\sqrt{a^2+b^2}[/tex]

## The Attempt at a Solution

[tex](\sqrt{3}(arccos\frac{\sqrt{3}}{3}+iarcsin\frac{\sqrt{6}}{3}))^5-(\sqrt{3}(arccos\frac{\sqrt{3}}{3}+iarcsin\frac{-\sqrt{6}}{3}))^5

[/tex]

How will I get integer angle out of here?

[tex]arccos\frac{\sqrt{3}}{3} \approx 54.74^\circ[/tex]

[tex]arcsin\frac{\sqrt{-6}}{3} \approx -54.74^\circ [/tex]