Write (i²⁵)³ in polar form.

Given Complex number is Z=(i²⁵)³

⇒ Z=i⁷⁵

⇒ Z=i⁷⁴.i

⇒ Z=(i²)³⁷.i

We know that i²=-1

⇒ Z=(-1)³⁷.i

⇒ Z=(-1).i

⇒ Z=-i

⇒ Z=0-i

We know that the polar form of a complex number Z=x+iy is given by Z=|Z|(cosθ+isinθ)

Where,

|Z|=modulus of complex number=

θ =arg(z)=argument of complex number=

Now for the given problem,

⇒

⇒

⇒

⇒ |z|=1

⇒

Since x>0,y<0 complex number lies in 4^th quadrant and the value of θ will be as follows -90⁰≤θ≤0⁰.

⇒

⇒ .

⇒

⇒

∴ The Polar form of Z=(i²⁵)³ is .