I'm confused how is -2+3i in polar form square root 13 (cos 2.159+ i sin 2.159)

Answer 1

Polar form is r ( cos x + i sin x)

r cos x = -2

r sin x = 3

To find r , square these and add

r² (cos² x + sin²x ) = 4 + 9 = 13

cos²x + sin²x =1 for any x, so r = √ 13

cos x = -2/√13, sin x = 3 / √13

because of the signs of these x must be in the 2nd quadrant

working in radians, x = cos^-1 (-1/ √13) = 2.159

you can check that sin 2.159 is in fact the required value

Answer 2

Check it out!