SOLUTION: find z/w and leave your answer in polar form. z=1+i and w=1-sqrt3i

Question 812669: find z/w and leave your answer in polar form. z=1+i and w=1-sqrt3i
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find z/w and leave your answer in polar form. z=1+i and w=1-sqrt3i
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z/w = [(1+i)(1+sqrt(3)i)]/[(1-sqrt(3)i)(1+sqrt(3)i)]
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= [1-sqrt(3)+(1+sqrt(3))i] / [1+3]
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= [(1-sqrt(3))/4] + (1+sqrt(3)/4]i
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Polar Form:
r^2 = [(1-sqrt(3))/4]^2 + [(1+sqrt(3))/4]^2 = 0.0335 + 0.4665 = 0.5
r = sqrt(0.5) = 0.7071
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theta = arctan[(1+sqrt(3))/(1-sqrt(3))] = arctan[(1+3)/(4-2sqrt(3))
= arctan[4/0.5359] = 82.37 degrees
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z/w = 0.7071(cos(82.37)+isin(82.37))
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Cheers,
Stan H.
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