# Answer on Complex Analysis Question for tyc

Question #25376

given z= -sqrt 5 + i

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

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

Expert's answer

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)

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)

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