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)

Then convert to x+iyx+iy using x=rcosθx=r\cos\theta and y=rsinθy=r\sin\theta.