Question

Question 5 Convert the given complex number in polar form: – 1 – i

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

Answer 1

Let z = -1 - i
we know, any complex number in the polar form is r(cos∅ + i sin∅) .
so,
-1 - i = r(cos∅ + isin∅)
-1 - i = rcos∅ +i rsin∅
rcos∅ = -1 _____________(1)
rsin∅ = -1_____________(2)
square and add equations (1) and (2)
r²( sin²∅ + cos²∅) = 1² + 1²
r².1 = 1 + 1 [ we know, sin²∅ + cos²∅ =1]
r = ±√2
but distance doesn't negative.
so, r = √2

divide (2) ÷ (1)
sin∅/cos∅ = 1
tan∅ = tan(π/4)
∅ = π/4
because ∅ lies on 3rd quadrant so,
arg(z) = -π + ∅
= -π + π/4
= -3π/4
thus,
z = -1 - i= √2[cos(-3π/4)+isin(-3π/4) ]