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Question Number 65983 by Rio Michael last updated on 07/Aug/19

$$Simplify$$$${(1+2i\sqrt{2})}^7-{(1+2i)}^7$$

Commented by Rio Michael last updated on 17/Aug/19

$$caniusede{moivre}^{\prime }stheorem?$$

Answered by MJS last updated on 07/Aug/19

$$\mathrm{well},\mathrm{just}\mathrm{do}\mathrm{it}!$$$${(1+b)}^7=1+7b+21b^2+35b^3+35b^4+21b^5+7b^6+b^7$$$$...$$$${(1+2\sqrt{2}\mathrm{i})}^7-{(1+2\mathrm{i})}^7=-1540-(278-1118\sqrt{2})\mathrm{i}$$

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