Complex Numbers Questions and Answers – Logarithm of Complex Numbers

This set of 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
View Answer

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

2. Find the value of log2(-3).
a) \(\frac{log⁡_3+i8\pi}{log_2}\)
b) \(\frac{log⁡_3+3i\pi}{log_2}\)
c) \(\frac{log⁡_3+i\pi}{log_2}\)
d) \(\frac{log_⁡2+i\pi}{log_3}\)
View Answer

Answer: c
Explanation: In this problem, we change the base to e
\(log_2(-3)=\frac{log_e(-3)}{loge(2)} \)

3. Represent ii in terms of e.
a) \(e^{\frac{-\pi}{3}}\)
b) \(e^{\frac{-3\pi}{2}}\)
c) \(e^{\frac{-\pi}{2}}\)
d) \(e^{\frac{-\pi}{6}}\)
View Answer

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,

Sanfoundry Global Education & Learning Series – Complex Analysis.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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