Question

Question 8 Convert the given complex number in polar form: i

Class X1 - Maths -Complex Numbers and Quadratic Equations Page 108

Answer 1

Let z = 0 + i
we know, any complex number in the polar form is r(cos∅ + i sin∅) .
so,
0 + i = r(cos∅ + isin∅)
0 + i = rcos∅ +i rsin∅
rcos∅ = 0 _____________(1)
rsin∅ = 1 _____________(2)
square and add equations (1) and (2)
r²( sin²∅ + cos²∅) = 0² + (-1)²
r².1 = 0 + 1 [ we know, sin²∅ + cos²∅ =1]
r = ±1
but distance doesn't negative.
so, r = 1

divide (2) ÷ (1)
sin∅/cos∅ = 1/0
tan∅ = tan(π/2)
∅ = π/2
because ∅ lies on 1st quadrant so,
arg(z) = ∅
= π/2
thus,
z = 0+ i= 1.[cos(π/2)+isin(π/2) ]