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FE ElectricalFree NCEES FE Electrical and Computer practice test
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Euler's formula states e^(j*theta) = cos(theta) + j*sin(theta). Using this identity, what is the value of e^(j*pi)?
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Q1. Euler's formula states e^(j*theta) = cos(theta) + j*sin(theta). Using this identity, what is the value of e^(j*pi)?
Correct answer: B. -1
Substituting theta = pi gives e^(j*pi) = cos(pi) + j*sin(pi) = -1 + j(0) = -1.
Q2. The complex number 3 + j4 is to be written in polar form as a magnitude at an angle. What is its magnitude?
Correct answer: C. 5
The magnitude is sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.
Q3. What is the complex conjugate of the number 2 + j5?
Correct answer: A. 2 - j5
The complex conjugate keeps the real part and negates the imaginary part, giving 2 - j5.
Q4. In complex-number arithmetic, what is the value of j squared (j^2)?
Correct answer: B. -1
The imaginary unit j is defined as sqrt(-1), so j^2 = -1.
Q5. According to the NCEES/NSPE code of ethics, what must engineers hold paramount above all other obligations?
Correct answer: B. The safety, health, and welfare of the public
The first fundamental canon requires engineers to hold paramount the safety, health, and welfare of the public.
Q6. An engineer discovers that a released design contains a defect that could endanger public safety, but the client insists it stay confidential. What is the ethically correct action?
Correct answer: C. Notify the appropriate authority to protect the public
The code of ethics places public safety above client confidentiality, so the engineer must disclose the hazard to the proper authority.
Q7. Using the single-payment compound-amount relationship F = P(1 + i)^n, what is the future worth of $1,000 invested for 1 year at an annual interest rate of 10%?
Correct answer: B. $1,100
F = 1000 * (1 + 0.10)^1 = 1000 * 1.10 = $1,100.
Q8. In engineering economics, which interest factor converts a present amount P into an equivalent future amount F?
Correct answer: A. The F/P single-payment compound-amount factor
The F/P factor multiplies a present value to obtain its equivalent future value.
Q9. What is the arithmetic mean of the data set 2, 4, 6, 8, and 10?
Correct answer: B. 6
The mean is (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.
Q10. In statistics, what does the standard deviation of a data set measure?
Correct answer: B. The spread or dispersion of values about the mean
Standard deviation quantifies how widely the data values are spread around the mean.
Exam facts and objectives sourced from the official NCEES (FE Exam) certification page. Last reviewed June 2026.
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