Question

Помогите, пожалуйста!
( (-1-√3 i)^57 )/( (1+i)^114 )

Answer 1

$\frac{(-1- \sqrt3i)^5^7}{(1+i)^1^1^4}= \frac{(2(cos \frac{4 \pi}{3}+isin \frac{4 \pi}{3}))^5^7}{( \sqrt{2}(cos \frac{ \pi}{4}+isin \frac{ \pi}{4}))^1^1^4}= \frac{2^5^7(cos(57* \frac{4 \pi}{3})+isin(57* \frac{4 \pi}{3}))}{(\sqrt2)^1^1^4(cos(114* \frac{ \pi}{4})+isin(114* \frac{ \pi}{4}))}=\\= \frac{2^5^7(cos76 \pi +isin76 \pi )}{2^5^7(cos \frac{57 \pi}{2}+isin \frac{57 \pi}{2})}= \frac{cos76 \pi+isin76 \pi}{cos \frac{57 \pi}{2}+isin \frac{57 \pi }{2}}=$$=\frac{cos0+isin0}{cos \frac{ \pi}{2}+isin \frac{ \pi}{2}}= \frac1i$
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