Theory of Intelligence
11TH•Mathematics•Complex Numbers•Exercise 1.5

Theory

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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

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