SOLUTION: Write the complex number in polar form with argument θ between 0 and 2π. −square root of 6+square root of 2 i

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Question 1135993: Write the complex number in polar form with argument θ between 0 and 2π.
−square root of 6+square root of 2 i

Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
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The modulus  r = %28-sqrt%286%29%29%5E2+%2B+%28sqrt%282%29%29%5E2%29 = sqrt%286+%2B+2%29 = sqrt%288%29 = 2%2Asqrt%282%29.


The argument  tan%28alpha%29 = -sqrt%282%29%2Fsqrt%286%29 = -1%2Fsqrt%283%29  =============>  alpha = 11pi%2F6.



Polar form:  -sqrt%286%29+%2B+sqrt%282%29%2Ai = %282%2Asqrt%282%29%29%2A%28cos%2811pi%2F6%29+%2B+i%2Asin%2811pi%2F6%29%29,   or   (r,alpha) = (2%2Asqrt%282%29,11pi%2F6).