Question

Find the value of log⁡(-6).

(a) log6+2iπ

(b) log⁡36+iπ

(c) log6+2iπ

(d) log6+iπ

I had been asked this question in an online quiz.

This interesting question is from Logarithm of Complex Numbers topic in portion Complex Numbers of Engineering Mathematics

Answer 1

The correct choice is (d) log6+iπ

The best I can explain: We know that

\(log⁡(x-iy)=\frac{1}{2} log⁡(x^2+y^2)+itan^{-1} (\frac{y}{x})\)

Putting x=-6 and y=0.

\(log⁡(-6)=\frac{1}{2} log⁡(36)+itan^{-1} (\frac{0}{-6})\)

\(log⁡(-6)=log6+iπ\).