How do you calculate 3(cos14^circ+isin14^circ)*2(cos121^circ+isin121^circ)3(cos14+isin14)2(cos121+isin121)?

1 Answer
Apr 6, 2017

Multiplication this type is defined as:

r_1(cos(theta_1)+isin(theta_1)*2(cos(theta_2)+isin(theta_2)=r_1r_2(cos(theta_1+theta_2)+isin(theta_1+theta_2))r1(cos(θ1)+isin(θ1)2(cos(θ2)+isin(θ2)=r1r2(cos(θ1+θ2)+isin(θ1+θ2))

Explanation:

In this case, r_1 = 3, r_2 = 2, theta_1 = 14^@", and "theta_2 =121^@r1=3,r2=2,θ1=14, and θ2=121:

3(cos14^circ+isin14^circ)*2(cos121^circ+isin121^circ) = 6(cos(135^@)+isin(135^@))3(cos14+isin14)2(cos121+isin121)=6(cos(135)+isin(135))

This simplifies to:

-3sqrt2+3sqrt2i32+32i