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Write the complex number in polar form with argument θ\theta between 00 and 2π2\pi. −2+2i-2 + 2i

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Convert complex numbers between rectangular and polar formright chevron icon

Full solution

Q. Write the complex number in polar form with argument θ\theta between 00 and 2π2\pi. −2+2i-2 + 2i
  1. Find Magnitude: Find the magnitude of the complex number.\newlineCalculate r=((−2)2+(2)2)r = \sqrt{((-2)^2 + (2)^2)}.\newliner=(4+4)r = \sqrt{(4 + 4)}.\newliner=8r = \sqrt{8}.\newliner=22r = 2\sqrt{2}.
  2. Calculate r: Find the argument of the complex number.\newlineCalculate θ=arctan⁡(y/x)=arctan⁡(2/(−2))\theta = \arctan(y/x) = \arctan(2/(-2)).\newlineθ=arctan⁡(−1)\theta = \arctan(-1).\newlineSince the complex number is in the second quadrant, add π\pi to the angle.\newlineθ=π+arctan⁡(−1)\theta = \pi + \arctan(-1).\newlineθ=π+(−π/4)\theta = \pi + (-\pi/4).\newlineθ=3π/4\theta = 3\pi/4.

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