#1**+10 **

The polar form can be written as.... z = r (cos Θ + i*sinΘ )

r = √[(4)^2 + (-4)^2] = √[16 + 16] = 4√2

And Θ = tan^{-1}(-4/4) = tan^{-1}(-1) = -pi/4 ...so we have

z = 4√2 ( cos (-pi/4) + i*sin (-pi/4) )

..... note that this is the principal value......any angle of the form -pi/4 + 2pi (n) is also possible, where n is an integer

CPhill
Jun 2, 2015

#1**+10 **

Best Answer

The polar form can be written as.... z = r (cos Θ + i*sinΘ )

r = √[(4)^2 + (-4)^2] = √[16 + 16] = 4√2

And Θ = tan^{-1}(-4/4) = tan^{-1}(-1) = -pi/4 ...so we have

z = 4√2 ( cos (-pi/4) + i*sin (-pi/4) )

..... note that this is the principal value......any angle of the form -pi/4 + 2pi (n) is also possible, where n is an integer

CPhill
Jun 2, 2015