SOLUTION: Multiply (sqrt(3) cis 15�)(2 cis 45�) and express the answer in rectangular coordinates. Give an exact answer.

Question 967543: Multiply (sqrt(3) cis 15�)(2 cis 45�) and express the answer in rectangular coordinates. Give an exact answer.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Multiply (sqrt(3) cis 15�)(2 cis 45�) and express the answer in rectangular coordinates. Give an exact answer.
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(sqrt(3)cis(15))(2cis(45)) = 2sqrt(3)cis(60)
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Ans::
sqrt(x^2+y^2] = 2
x^2 + y^2 = 4
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60 = arctan(y/x)
y/x = tan(60) = sqrt(3)
x = y/sqrt(3)
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Substitute and solve for "y"::
[y^2/3 + y^2] = 4
(4/3)y^2 = 4
(1/3)y^2 = 1
y^2 = 3
y = sqrt(3)
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Solve for "x"::
x = y/sqrt(3) = sqrt(3)/sqrt(3) = 1
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Ans:: x+yi = 1+sqrt(3)i
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Cheers,
Stan H.
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