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

Theory

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Theory

  • If z1=r1(cos⁡θ1+isin⁡θ1)z_1=r_1(\cos\theta_1+i\sin\theta_1) and z2=r2(cos⁡θ2+isin⁡θ2)z_2=r_2(\cos\theta_2+i\sin\theta_2) then:
z1z2=r1r2(cos⁡(θ1+θ2)+isin⁡(θ1+θ2))z_1z_2=r_1r_2\left(\cos(\theta_1+\theta_2)+i\sin(\theta_1+\theta_2)\right) z1z2=r1r2(cos⁡(θ1−θ2)+isin⁡(θ1−θ2))\frac{z_1}{z_2}=\frac{r_1}{r_2}\left(\cos(\theta_1-\theta_2)+i\sin(\theta_1-\theta_2)\right)
  • For z1±z2z_1\pm z_2, first convert to rectangular form and then add/subtract.

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