# The Complex Exponential MCQ’s

This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “The Complex Exponential”.

1. What is the magnitude of exp(2+3j)?

a) exp(2.3)

b) exp(3)

c) exp(2)

d) exp(3/2)

2. What is the fundamental frequency of exp(2pi*w*j)?

a) 1pi*w

b) 2pi*w

c) w

d) 2w

3. What is exp(ja) equal to, where j is the square root of unity?

a) cos ja + jsin a

b) sin a + jcos a

c) cos j + a sin j

d) cos a + jsin a

4. Total energy possessed by a signal exp(jwt) is?

a) 2pi/w

b) pi/w

c) pi/2w

d) 2pi/3w

5. What is the power possessed by a signal exp(jwt)?

a) 1

b) 0.5

c) ^{1}⁄_{w}

d) w

6. exp(jwt) is periodic

a) for any w

b) for any t

c) for no w

d) for no t

7. Sinusoidal signals multiplied by decaying exponentials are referred to as

a) Amplified sinusoids

b) Neutralized sinusoids

c) Buffered sinusoids

d) Damped sinusoids

8. What is the period of exp(2+pi*j/4)t?

a) 4

b) 8

c) 16

d) 20

9. Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?

a) 8

b) 12

c) 18

d) 24

10. The most general form of complex exponential function is:

a) e^{σt}

b) e^{Ωt}

c) e^{st}

d) e^{at}

11. When is a complex exponential signal sinusoidal?

a) σ =0 and Ω = 0

b) σ < 0 and Ω = 0

c) σ = 0 and Ω ≠ 0

d) σ ≠ 0 and Ω ≠ 0

12. exp[jwn] is periodic

a) for any w

b) for any t

c) for w=2pi*M/n

d) for t = 1/w

13. A complex exponential signal is a decaying exponential signal when

a) Ω = 0 and σ > 0

b) Ω = 0 and σ = 0

c) Ω ≠ 0 and σ < 0

d) Ω = 0 and σ < 0

14. An exponentially growing sinusoidal signal is:

a) σ = 0 and Ω = 0

b) σ > 0 and Ω ≠ 0

c) σ < 0 and Ω ≠ 0

d) σ = 0 and Ω ≠ 0

15. Determine the nature of the signal: x(t) = e^{-0.2t} [cosΩt + jsinΩt].

a) Exponentially decaying sinusoidal signal

b) Exponentially growing sinusoidal signal

c) Sinusoidal signal

d) Exponential signal

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