Question

If Z = 2(cos95 - isin95)
Find Z^2

Answer 1

So we have:


`\sf (2(cos(95\textdegree)- i sin(95\textdegree)))^2`

Convert to radians:


`\sf (2(cos((19)/(36)\pi)- i sin((19)/(36)\pi)))^2`

Use the identity:
`\sf cos(x)-isin(x)=e^(-ix)`


`\sf (2e^{-i(19)/(36)\pi})^2`

Simplify:


`\sf e^{-i(19)/(36)\pi}=\frac{1}{(-1)^{(19)/(36)}}`


`\sf (2*\frac{1}{(-1)^{(19)/(36)}})^2\rightarrow \boxed{\sf 4(-1)^{(17)/(18)}}`