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
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