Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.5

Theory

  • If z1=r1(cosθ1+isinθ1)z_1=r_1(\cos\theta_1+i\sin\theta_1) and z2=r2(cosθ2+isinθ2)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(θ1θ2)+isin(θ1θ2))\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.