Friday
July 25, 2014

Homework Help: Complex angles

Posted by Mathslover on Wednesday, May 29, 2013 at 11:54pm.

There are four complex fourth roots to the number 4−43√i. These can be expressed in polar form as

z1=r1(cosθ1+isinθ1)
z2=r2(cosθ2+isinθ2)
z3=r3(cosθ3+isinθ3)
z4=r4(cosθ4+isinθ4),

where ri is a real number and 0∘≤θi<360∘. What is the value of θ1+θ2+θ3+θ4 (in degrees)?

Details and assumptions
i is the imaginary unit satisfying i2=−1.

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