Question

Question 6 Convert the given complex number in polar form: –3

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

Answer 1

Let z = -3 + 0.i
we know, any complex number in the polar form is r(cos∅ + i sin∅) .
so,
-3 + 0.i = r(cos∅ + isin∅)
-3 + 0.i= rcos∅ +i rsin∅
rcos∅ = -3 _____________(1)
rsin∅ = -0_____________(2)
square and add equations (1) and (2)
r²( sin²∅ + cos²∅) = (-3)² + 0
r².1 = 9 +0 [ we know, sin²∅ + cos²∅ =1]
r = ±3
but distance doesn't negative.
so, r = 3

divide (2) ÷ (1)
sin∅/cos∅ = 0
tan∅ = tan(0)
∅ = 0
because ∅ lies on 2nd quadrant so,
arg(z) = π-∅
= π - 0
= π
thus,
z = -1 - i= 3 [cos(π) +isin(π ) ]