Complex NumbersHard
Question
Let z is a complex number such that 
= and arg(z) = θ, then maximum value of cos(2θ) is -
= and arg(z) = θ, then maximum value of cos(2θ) is -Options
A.
B.0
C.
D.1
Solution
|3r cos θ + (3r sin θ)i + 
| = 2
9r2 +
+ 6(cos2θ - sin2θ) = 4
6 cos 2θ = 4 -
cos 2θ =
≥ 3 ⇒ 9r2 + 
≥ 6
maximum value of cos 2θ = -
| = 29r2 +
+ 6(cos2θ - sin2θ) = 46 cos 2θ = 4 -
cos 2θ =
≥ 3 ⇒ 9r2 + ≥ 6 maximum value of cos 2θ = -
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