Find the modulus and argument of .

Given complex number is

⇒

⇒

⇒

We know that i²=-1

⇒

⇒

⇒ z=-4+i4

We know that the polar form of a complex number Z = x + iy is given by Z = |Z| (cos θ + i sin θ)

Where,

|Z|=modulus of complex number=

θ =arg(z)=argument of complex number=

Now for the given problem,

⇒

⇒

⇒

⇒ |z|=8

⇒

Since x<0, y>0 complex number lies in 2^nd quadrant and the value of θ will be as follows 90⁰≤θ≤180⁰.

⇒

⇒ .

⇒

∴ The Polar form of is .