Answer to Question #25376 in Complex Analysis for tyc

Question

given z= -sqrt 5 + i
express z = -sqrt 5 + i in the form of r(cost tita + sin teta)

Answer 1

Let z=a+b*i, then a=-sqrt 5 and b=1
r=sqrt(a^2 +b^2)=sqrt(5+1)=sqrt 6
tan teta = b/a=-1/sqrt 5=-(sqrt 5)/5
We can see that teta is in a second quadrant, then teta=180 + tan^-1(-(sqrt5)/5) = 180 - 24.1=155.9 degrees
Answer: z = sqrt 6*(cos 155.9 +i*sin 155.9)