Precalculus: Find z. w and z/w. Write your answer in both polar form and exponential form.

Question

Let z=2(cos 2pi/3 + isin 2pi/3),w=4(cos 5pi/9 + isin 5pi/9).

Find z. w and z/w. Write your answer in both polar form and exponential form.

Answer 1

Hi Katelyn A.,

For z = 2[cos(2π/3) + i sin(2π/3)]; w = 4[cos(5π/9) + i sin(5π/9)]:

z*w = 2*4[cos(2π/3 +5π/9) + i sin(2π/3 + 5π/9)]

z*w = 8[cos(11π/9) + i sin(11π/9)], (polar form)

z*w = 8e^i(11π/9), (exponential form)

z/w = 2/4[cos(2π/3 - 5π/9) + i sin(2π/3 - 5π/9)]

z/w = 1/2[cos(π/9) + i sin(π/9)]

z/w = (1/2)e^i(π/9)

I hope this helps, Joe.

Answer 2

A formula for the devision of complex numbers is given in your text book. Do you have a specific question as to how to implement it?