250+ TOP MCQs on Logarithm of Complex Numbers and Answers

Complex Analysis Questions and Answers for Campus interviews focuses on “Logarithm of Complex Numbers”.

1. Find the value of log⁡(-6).
a) log6+2iπ
b) log⁡36+iπ
c) log6+2iπ
d) log6+iπ
Answer: d
Explanation: 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).

2. Find the value of log₂(-3).
a) (frac{log⁡_3+i8pi}{log_2})
b) (frac{log⁡_3+3ipi}{log_2})
c) (frac{log⁡_3+ipi}{log_2})
d) (frac{log_⁡2+ipi}{log_3})
Answer: c
Explanation: In this problem, we change the base to e
(log_2(-3)=frac{log_e(-3)}{loge(2)} )
(log_2(-3)=frac{log⁡_3+ipi}{log_2}).

3. Represent iⁱ in terms of e.
a) (e^{frac{-pi}{3}})
b) (e^{frac{-3pi}{2}})
c) (e^{frac{-pi}{2}})
d) (e^{frac{-pi}{6}})
Answer: c
Explanation: We know that
(a^x=e^{x loga})
(i^i=e^{i log⁡i})
We also know from the definition of logarithm,
(log⁡i=frac{ipi}{2})
(i^i=e^{i(frac{ipi}{2})}=e^{frac{-pi}{2}}).

Global Education & Learning Series – Complex Analysis.

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