SOLUTION: Can someone PLEASE help me with this problem?! THANK YOU! Find all the square roots of the complex number -3-2i. Write the square roots in polar (re^(i(theta))) form, with t

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Can someone PLEASE help me with this problem?! THANK YOU! Find all the square roots of the complex number -3-2i. Write the square roots in polar (re^(i(theta))) form, with t      Log On


   

Question 615356: Can someone PLEASE help me with this problem?! THANK YOU!
Find all the square roots of the complex number -3-2i.
Write the square roots in polar (re^(i(theta))) form, with the smaller angle first. Give your angles in degrees.
Root 1)=?
Root 2)=?
Write the square roots in a+bi form, with the smaller angle first.
Root 1)=?
Root 2)=?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find all the square roots of the complex number -3-2i.
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z = -3-2i
r+=+sqrt%283%5E2+%2B+2%5E2%29+=+sqrt%2813%29
theta = atan(2/3) =~ 213.69 degs
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z = sqrt(13)cis(theta)
sqrt%28z%29+=+root%284%2C13%29cis%28theta%2F2%29
= 1.89883*cis(106.84)
= -0.55 + i*1.817
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sqrt%28z%29+=+root%284%2C13%29cis%28%28theta%2F2%29+%2B+180%29%29
= 1.89883*cis(286.845)
= 0.55 - i*1.817