Question

find the polar form of z= i​

Answer 1

follows: The polar form of a complex number z=a+bi is z=r(cosθ+isinθ) , where r=|z|=√a2+b2 , a=rcosθ and b=rsinθ , and θ=tan−1(ba) for a>0 and θ=tan−1(ba)+π or θ=tan−1(ba)+180° for a<0 . Example: Express the complex number in polar form.

Answer 2

Step-by-step explanation:

z=i

Let rcosθ=0 and rsinθ=1

On squaring and adding, we obtain

r2cos2θ+r2sin2θ=02+12

⇒r2(cos2θ+sin2θ)=1

⇒r2=1

⇒r=1=1 (Since, r>0)

∴cosθ=0 and sinθ=1

∴θ=2π

So, the polar form is 

∴i=rcosθ+irsinθ=cos2π+isin2π