schoolAccedmy
Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.5

Theory

  • If z=r(cos⁡θ+isin⁡θ)z=r(\cos\theta+i\sin\theta) then:
Re⁡(z)=rcos⁡θ,Im⁡(z)=rsin⁡θ\operatorname{Re}(z)=r\cos\theta,\quad \operatorname{Im}(z)=r\sin\theta
  • Use angle identities:
cos⁡(−θ)=cos⁡θ,sin⁡(−θ)=−sin⁡θ\cos(-\theta)=\cos\theta,\quad \sin(-\theta)=-\sin\theta
arrow_back
Previous
Exercise 1.4