Complex Analysis MCQs Math

\[
\textbf{MCQs on Complex Analysis with Answers}
\]

\[
\textbf{Q1: Which of the following is a complex number?}
\]
\[
\text{(A) } 5 \quad
\text{(B) } 2 + 3i \quad
\text{(C) } \sqrt{2} \quad
\text{(D) } 0
\]
\[
\textbf{Answer: (B) } 2 + 3i
\]

\[
\textbf{Q2: The complex conjugate of } z = a + bi \text{ is:}
\]
\[
\text{(A) } a – bi \quad
\text{(B) } -a + bi \quad
\text{(C) } a + bi \quad
\text{(D) } 0
\]
\[
\textbf{Answer: (A) } a – bi
\]

\[
\textbf{Q3: Which of the following is a representation of a complex number in polar form?}
\]
\[
\text{(A) } z = r (\cos \theta + i \sin \theta) \quad
\text{(B) } z = r e^{i\theta} \quad
\text{(C) } z = a + bi \quad
\text{(D) } Both (A) and (B)
\]
\[
\textbf{Answer: (D) } Both (A) and (B)
\]

\[
\textbf{Q4: The modulus of a complex number } z = 3 + 4i \text{ is:}
\]
\[
\text{(A) } 3 \quad
\text{(B) } 4 \quad
\text{(C) } 5 \quad
\text{(D) } 7
\]
\[
\textbf{Answer: (C) } 5
\]

\[
\textbf{Q5: If } f(z) = z^2 \text{, what is the derivative of } f(z) \text{ with respect to } z \text{?}
\]
\[
\text{(A) } 2z \quad
\text{(B) } 1 \quad
\text{(C) } z \quad
\text{(D) } 0
\]
\[
\textbf{Answer: (A) } 2z
\]

\[
\textbf{Q6: Which of the following statements is true about a meromorphic function?}
\]
\[
\text{(A) } It is analytic everywhere except at isolated singularities. \quad
\text{(B) } It is not analytic at any point. \quad
\text{(C) } It has no singularities. \quad
\text{(D) } It is analytic at all points.
\]
\[
\textbf{Answer: (A) } It is analytic everywhere except at isolated singularities.
\]

\[
\textbf{Q8: If } f(z) = \frac{1}{z}, \text{ the singularity at } z = 0 \text{ is:}
\]
\[
\text{(A) } A removable singularity \quad
\text{(B) } A pole \quad
\text{(C) } An essential singularity \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (B) } A pole
\]

\[
\textbf{Q9: Which of the following is true for an entire function?}
\]
\[
\text{(A) } It has isolated singularities. \quad
\text{(B) } It is analytic everywhere in the complex plane. \quad
\text{(C) } It has singularities at some points in the complex plane. \quad
\text{(D) } It is not differentiable at any point.
\]
\[
\textbf{Answer: (B) } It is analytic everywhere in the complex plane.
\]

\[
\textbf{Q10: The Cauchy-Riemann equations are used to determine whether a function is:}
\]
\[
\text{(A) } Continuous \quad
\text{(B) } Analytic \quad
\text{(C) } Differentiable \quad
\text{(D) } Integrable
\]
\[
\textbf{Answer: (B) } Analytic
\]