Complex NumbersHard
Question
The curve represented by z = 
, θ ∈ [0, 2π)
, θ ∈ [0, 2π)Options
A.never meets the imaginary axis
B.meets the real axis in exactly two points
C.has maximum value of |z| as 3
D.has minimum value of |z| as 1
Solution
z = 
For imaginary axis, real part = 0 i.e. 2 + cos θ = 0 which is not possible, so curve never meets the imaginary axis
For real axis Im z = 0 ⇒ sin θ = 0 ⇒ θ = 0, π ∈ [0, 2π), so curve meets the real axis in two points.
|z| = 3.
= 3(5 + 4 cosθ)-1/2 ⇒ |z|max = 3, |z|min = 1
For imaginary axis, real part = 0 i.e. 2 + cos θ = 0 which is not possible, so curve never meets the imaginary axis
For real axis Im z = 0 ⇒ sin θ = 0 ⇒ θ = 0, π ∈ [0, 2π), so curve meets the real axis in two points.
|z| = 3.
= 3(5 + 4 cosθ)-1/2 ⇒ |z|max = 3, |z|min = 1Create a free account to view solution
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