This set of Engineering Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Logarithm of Complex Numbers”.
1. Find the value of log(-6).
a) log6+2iπ
b) log36+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.
\(log(-6)=\frac{1}{2} log(36)+itan^{-1} (\frac{0}{-6})\)
\(log(-6)=log6+iπ\).
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) \(\frac{log_3+i8\pi}{log_2}\)
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
\(log_2(-3)=\frac{log_e(-3)}{loge(2)} \)
\(log_2(-3)=\frac{log_3+i\pi}{log_2}\).
Explanation: In this problem, we change the base to e
\(log_2(-3)=\frac{log_e(-3)}{loge(2)} \)
\(log_2(-3)=\frac{log_3+i\pi}{log_2}\).
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
\(a^x=e^{x loga}\)
\(i^i=e^{i logi}\)
We also know from the definition of logarithm,
\(logi=\frac{i\pi}{2}\)
\(i^i=e^{i(\frac{i\pi}{2})}=e^{\frac{-\pi}{2}}\).
Explanation: We know that
\(a^x=e^{x loga}\)
\(i^i=e^{i logi}\)
We also know from the definition of logarithm,
\(logi=\frac{i\pi}{2}\)
\(i^i=e^{i(\frac{i\pi}{2})}=e^{\frac{-\pi}{2}}\).
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Sanfoundry Global Education & Learning Series – Complex Analysis.
To practice all areas of Engineering Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.
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