Question

Write (i²⁵)³ in polar form.

Answer 1

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= \(\sqrt{x^2+y^2}\)

θ =arg(z)=argument of complex number= tan^-1\(\Big(\frac{|y|}{|x|}\Big)\)

Now for the given problem,

Since x>0,y<0 complex number lies in 4^th quadrant and the value of θ will be as follows -90 °≤θ≤0°.