SOLUTION: Question 1 Z1=3+2j Z2=1+7j A. Find Z1xZ2 B. Find Z1/Z2 Question 2 Convert Z1 and Z2 into polar and find the following A. Find Z1xZ2 B. Find Z1/Z2 Please answer

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Question 1 Z1=3+2j Z2=1+7j A. Find Z1xZ2 B. Find Z1/Z2 Question 2 Convert Z1 and Z2 into polar and find the following A. Find Z1xZ2 B. Find Z1/Z2 Please answer      Log On


   

Question 935628: Question 1
Z1=3+2j Z2=1+7j
A. Find Z1xZ2
B. Find Z1/Z2
Question 2
Convert Z1 and Z2 into polar and find the following
A. Find Z1xZ2
B. Find Z1/Z2
Please answer in as much detail as possible and show all working for both questions.
Thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the FOIL method,
%283%2B2j%29%281%2B7j%29=3%2B21j%2B2j%2B14j%5E2
%283%2B2j%29%281%2B7j%29=%283-14%29%2B23j
%283%2B2j%29%281%2B7j%29=-11%2B23j
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%283%2B2j%29%281%2B7j%29=%28%283%2B2j%29%2F%281%2B7j%29%29%28%281-7j%29%2F%281-7j%29%29
%283%2B2j%29%281%2B7j%29=%28%283%2B2j%29%281-7j%29%29%2F%28%281%2B7j%29%281-7j%29%29
%283%2B2j%29%281%2B7j%29=%283-21j%2B2j-14j%5E2%29%2F%281-7j%2B7j-49j%5E2%29
%283%2B2j%29%281%2B7j%29=%2817-19j%29%2F%2850%29
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Z%5B1%5D
R%5B1%5D=sqrt%283%5E2%2B2%5E2%29=sqrt%2813%29
alpha=tan%5E%28-1%29%282%2F3%29=33.7
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Z%5B2%5D
R%5B2%5D=sqrt%281%5E2%2B7%5E2%29=sqrt%2850%29=5sqrt%282%29
beta=tan%5E%28-1%29%287%2F1%29=81.9
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Z%5B1%5D%2AZ%5B2%5D=5sqrt%2826%29%2A%28cos%28115.6%29%2Bi%2Asin%28115.6%29%29
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Z%5B1%5D%2FZ%5B2%5D=%28sqrt%2826%29%2F10%29%2A%28cos%28-48.2%29%2Bi%2Asin%28-48.2%29%29
Z%5B1%5D%2FZ%5B2%5D=%28sqrt%2826%29%2F10%29%2A%28cos%28311.8%29%2Bi%2Asin%28311.8%29%29