SOLUTION: Let z1 = 1 - i√3 and z2 = -1 + i√3. a) Express z1z2 in rectangular form. b) Express z1, z2, and z1z2 in polar form. c) Show that your answers to Part A and Part B are the sa

Algebra ->  Trigonometry-basics -> SOLUTION: Let z1 = 1 - i√3 and z2 = -1 + i√3. a) Express z1z2 in rectangular form. b) Express z1, z2, and z1z2 in polar form. c) Show that your answers to Part A and Part B are the sa      Log On


   

Question 1138181: Let z1 = 1 - i√3 and z2 = -1 + i√3.
a) Express z1z2 in rectangular form.
b) Express z1, z2, and z1z2 in polar form.
c) Show that your answers to Part A and Part B are the same.
Make sure to show work.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(a)

(b)

z1 = 1-1*sqrt(3):
r+=+sqrt%281%5E2%2B%28sqrt%283%29%29%5E2%29+=+sqrt%281%2B3%29+=+2
theta+=+arctan%28%28-1%2Asqrt%283%29%29%2F1%29+=+-pi%2F3 (because z1 is in quadrant IV)
z1 = (2,-pi/3)

z2 = -1+i*sqrt(3):
r+=+sqrt%281%5E2%2B%28sqrt%283%29%29%5E2%29+=+sqrt%281%2B3%29+=+2
theta+=+arctan%28%28-1%2Asqrt%283%29%29%2F1%29+=+2pi%2F3 (because z2 is in quadrant II)
z1 = (2,2pi/3)


z1*z2 = (2,-pi/3)*(2,2pi/3) = (4,pi/3)

c) (4,pi/3) =