82 Write the complex number in trigonometric form Round the

8.2

Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. (Do not use cis form.) 5 - 12i

Solution

given 5 - 12 i = x + y i (say

then x = 5, y= -12

then z = sqrt(x^2+y^2) , t = arctan(y/x)

z = sqrt(25+144) , t =arctan(-12/5)

z = 13 , t = -67.38 degress

now trigonometric form of 5 - 12 i is 13[ cos(-67.38) + i sin(-67.38) ]