Question

How do you perform the operation in trigonometric form `(cos50+isin50)/(cos20+isin20)`?

Answer 1

`1/2(i+sqrt3)`

Explanation:

`(cos50+isin50)/(cos20+isin20)= ((cos50+isin50)(cos20-isin20))/((cos20+isin20)(cos20-isin20)) = (cos50cos20+i(sin50cos20-sin20cos50) - i^2sin50sin20)/(cos^2 20-i^2sin^20) =(cos50cos20+i(sin50cos20-sin20cos50) +sin50sin20)/(cos^2 20+sin^2 20) =(cos(50-20)+isin(50-20))/1=cos30+isin30=sqrt3/2+i*1/2=1/2(i+sqrt3)`since `i^2=-1`[Ans]