Complex Numbers Which form is better for adding complex numb

Complex Numbers Which form is better for adding complex numbers, rectangular or polar? Add Z_1 = 2e^j45 degree and Z_2 = Se^-j30degree together. Write your result in both rectangular and polar form, indicate if your angle is in degrees or radians. Which form is better for multiplying complex numbers, rectangular or polar? Multiply Z_1 = -5+j2 and Z_2 = 3 + j9 together. Write your result in both rectangular and polar form, indicate if your angle is in degrees or radians.

Solution

a) Rectangular form is better for adding complex numbers

b) Z₁ in polar form = 2 cos45^o + j2 sin45^o

                           =1.414 + j1.414

    Z₂ in polar form = 5 cos30^o - j5 sin30^o
                       =4.33 -j2.5

Z₁+Z₂ = 5.744 - j1.086 (Rectangular form)

Z₁+Z₂ = 5.845 e^-j10.7o (Polar form)

c) Polar form is better for multiplying two complex numbers

d) Z₁+Z₂ = (-5 + j2) X (3 +j9)

             = -15-j45+j6-18

             = -33 -j39 (Rectangular form)

    Z₁+Z₂ = 142.86 e^-j103.35 (polar form)