GRE Subject Test: Math : Complex Plane

Example Questions

Example Question #162 : Imaginary Numbers

Write the complex number  in polar form, that is, in terms of a distance from the origin  on the complex plane and an angle from the positive -axis, , measured in radians.

Explanation:

To see what the polar form of the number is, it helps to draw it on a graph, where the horizontal axis is the imaginary part and the vertical axis the real part. This is called the complex plane.

To find the angle , we can find its supplementary angle  and subtract it from  radians, so .

Using trigonometric ratios,    and  .

Then .

To find the distance , we need to find the distance from the origin to the point . Using the Pythagorean Theorem to find the hypotenuse  or .