GRE Subject 2026 Practice Test Maths Complex Analysis Free Quiz 1

1. What does complex analysis study?

A. Functions of complex variables B. Real analysis C. Abstract algebra D. Differential equations

2. What is the value of i^2 in complex numbers?

A. i^2 = 1 B. i^2 = 0 C. i^2 = -1 D. i^2 = i

3. What is the conjugate of z = x + iy?

A. -x + iy B. x - iy C. -x - iy D. x + iy

4. What is the modulus of z = x + iy?

A. √(x^2 + y^2) B. x^2 + y^2 C. √(x^2 - y^2) D. x^2 - y^2

5. What is the argument of a complex number?

A. |z| B. Re(z) C. Arg(z) D. Im(z)

6. What is Euler's formula?

A. e^(iθ) = cos θ - i sin θ B. e^(iθ) = sin θ + i cos θ C. e^(iθ) = cos θ D. e^(iθ) = cos θ + i sin θ

7. What are the Cauchy-Riemann equations?

A. Sufficient conditions B. Necessary and sufficient C. Necessary conditions D. Not necessary

8. What are the Cauchy-Riemann equations?

A. u_x = -v_y, u_y = v_x B. u_x = v_y, u_y = v_x C. u_x = -v_y, u_y = -v_x D. u_x = v_y, u_y = -v_x

9. What is a point where a function is not analytic?

A. Zero B. Singularity C. Pole D. Essential singularity

10. What type of singularity has the function going to infinity?

A. Pole B. Removable C. Essential D. Branch point