Convert each of the given numbers in the polar form rcis the

Convert each of the given numbers in the polar form rcis theta, -pi

Solution

a) ( 8 -i)/3

r = sqrt((8/3)^2 + (1/3)^2) = sqrt(65/9) = sqrt(65)/3

theta = tan^-1(-1/3/8/3) = tan^-1(-1/8) = -0.124 radians

b) theta = tan^-1(-4pi*sqrt3/-4pi) = pi/3 = 1.047 radians

c) theta = 7tan^-1(1) =7pi/4 = 5.498 radians