Evaluate cos115degree isin115degreecos 70degree isin 70deg

Evaluate: cos115degree + isin115degree/cos 70degree + isin 70degree

Solution

(cos115^o +isin115^o)/(cos70^o+isin70^o)

=eⁱ¹¹⁵/eⁱ⁷⁰

=e^(115-70)i

=e⁴⁵ⁱ

=(cos45^o +isin45^o)

=(1/2 +i/2)

=(1/2)(1+i)