SOLUTION: Divide the complex numbers in two ways, first by leaving them in rectangular form, then by switching to cis form. Show that you get the same answer working in both rectangular and

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: Divide the complex numbers in two ways, first by leaving them in rectangular form, then by switching to cis form. Show that you get the same answer working in both rectangular and       Log On


   

Question 1078163: Divide the complex numbers in two ways, first by leaving them in rectangular form, then by switching to cis form. Show that you get the same answer working in both rectangular and polar forms. +%28-6i%29%2F%28-1%2B+sqrt%28+3i%29%29+.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!




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So convert to polar coordinates,
(0,-6)
R%5B1%5D=6
theta%5B1%5D=270
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(-1,sqrt(3))
R%5B2%5D=sqrt%28%28-1%29%5E2%2B%28sqrt%283%29%29%5E2%29=sqrt%281%2B3%29=sqrt%284%29=2
theta%5B2%5D=tan%5E%28-1%29%28sqrt%283%29%2F1%29=120
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So then,
Magnitude:
Z%5B1%5D%2FZ%5B2%5D=%28R%5B1%5D%2FR%5B2%5D%29=6%2F2=3
Angle:
Z%5B1%5D%2FZ%5B2%5D=270-120=150
All together,
Z%5B1%5D%2FZ%5B2%5D=3cos%28150%29%2Bi%283sin%28150%29%29
Z%5B1%5D%2FZ%5B2%5D=3%28-sqrt%283%29%2F2%29%2Bi%283%281%2F2%29%29
Z%5B1%5D%2FZ%5B2%5D=%283%2F2%29%28-sqrt%283%29%2Bi%29
Z%5B1%5D%2FZ%5B2%5D=-%283%2F2%29%28sqrt%283%29-i%29