Question

Convert the following complex number into its polar representation: 2-2sqrt3i

Answer 1

Answer:

  C.  4(cos(300°) +i·sin(300°))

Step-by-step explanation:

The magnitude will be ...

  magnitude = √(2^2 +(-2√3)^2) = √(4+12) = 4

The negative imaginary part puts the angle in the 4th quadrant. The answer choice with a magnitude of 4 and a 4th-quadrant angle is ...

  4(cos(300°) +i·sin(300°))

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If you want to figure the angle, it will be ...

  angle = arctan(Im()/Re()) = arctan(-2√3/2) = arctan(-√3) = -60°

The corresponding 4th-quadrant angle is 300°.

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Comment on answer choices

Answer choice A is another representation of the same number. Typically, we want the magnitude to be positive in polar form, so that answer can be avoided on those grounds.