Question

The polar form of a complex number z = a+bi is z = r(cosθ+isinθ) , where r = |z| = sqrt(a^2+b^2) , a = rcosθ  and  b = rsinθ and θ = tan^−1(b/a)  for a > 0 and θ = tan^−1(b/a ) + π or θ = tan^−1(b/a) +180° for a < 0. What is the value for  θ = tan^−1(b/a)  for a = 0?

Example: Express z = 0 + i in polar from with the principal argument. The principal argument is π/2. How did they get π/2 when a = 0?

Answer 1

WELCOME

GIVEN

Z = 0 + i

compairing a + bi we get
a = 0
b = 1

r= √(1+0) = 1
Θ = tan-1 (b/a)
= tan-1 (1/0)
= tan-1(∞)
= tan-1(π/2)
= π/2
Thus z = 0 + i
= r(cos Θ + isin Θ)
= cos π/2 + isin π/2