Question
Mathematics Question on Logarithmic Differentiation
The general value of the real angle θ, which satisfies the equation, (cosθ + i sinθ) (cos2θ + i sin2θ)........ (cosnθ + i sinnθ) = 1 is given by, (assuming k is an integer)
A
n+22kπ
B
n(n+1)4kπ
C
n+14kπ
D
n(n+1)6kπ
Answer
n(n+1)4kπ
Explanation
Solution
The correct option is(C): n(n+1)4kπ.
eiθ⋅ei(2θ)⋅ei(3θ)…ei(nθ)=1⇒ei(θ2(n(n+1)))=ei2kπ⇒θ=n(n+1)4kπ