If \(A = 40 e^{j120^\circ}\), \(B = 20\angle -40^\circ\), \(C = 26.46 + j0\), solve for \(A + B + C\).
A\(27.7\angle 45^\circ\)
B\(35.1\angle 45^\circ\)
C\(30.8\angle 45^\circ\)
D\(33.4\angle 45^\circ\)
Mathematics · Question Bank
Advanced Engineering Mathematics
16 of 84 questions match. Answer in your head first, then check the solution.
What is the simplified complex expression of \((4.33 + j2.5)^2\)?
A12.5 + j21.65
B20 + j20
C15 + j20
D21.65 + j12.5
Find the value of \((1+i)^5\), where i is an imaginary number.
A1-i
B-4(1+i)
C1+i
D4(1+i)
Find the principal \(5^{\text{th}}\)-root of \([50(\cos 150^\circ + j \sin 150^\circ)]\).
A1.9 + j1.1
B3.26 - j2.1
C2.87 + j2.1
D2.25 - j1.2
Simplify \(\frac{(2+3i)(5-i)}{(3-2i)^2}\)
A\(\frac{221-91i}{169}\)
B\(\frac{21+52i}{13}\)
C\(\frac{-7+17i}{13}\)
D\(\frac{-90+220i}{169}\)
Three vectors A, B and C are related as follows: \(\frac{A}{B} = 2\text{ at } 180^\circ\), \(A+C = -5+j15\), \(C = \text{conjugate of } B\). Find A.
A5 - j5
B-10 + j10
C10 - j10
D15 + j15
Evaluate \(\ln(2+j3)\)
A1.34 + j0.32
B2.54 + j0.866
C2.23 + j0.21
D1.28 + j0.98
Evaluate the determinant: \(\begin{vmatrix} 2 & 14 & 3 & 1 \\ 1 & 5 & -1 & 3 \\ 1 & -2 & 2 & -3 \\ 3 & -4 & -3 & -4 \end{vmatrix}\)
A489
B389
C326
D452
Compute the value of x by determinant: \(x = \begin{vmatrix} 4 & -1 & 2 & 3 \\ 2 & 0 & 2 & 1 \\ 10 & 3 & 0 & 1 \\ 14 & 2 & 4 & 5 \end{vmatrix}\)
A-32
B-28
C16
D52
Given the equations:
\(x+y+z=2\)
\(3x-y-2z=4\)
\(5x-2y+3z=-7\)
Solve for y by determinants.
\(x+y+z=2\)
\(3x-y-2z=4\)
\(5x-2y+3z=-7\)
Solve for y by determinants.
A1
B-2
C3
D0
Solve the equations by Cramer's Rule:
\(2x-y+3z=-3\)
\(3x+3y-z=10\)
\(-x-y+z=-4\)
\(2x-y+3z=-3\)
\(3x+3y-z=10\)
\(-x-y+z=-4\)
A(2, 1, -1)
B(2, -1, -1)
C(1, 2, -1)
D(-1, -2, 1)
Determine the inverse Laplace transform of \(I(s) = \frac{200}{s^2 - 50s + 10625}\)
A\(I(t) = 2e^{25t} \sin 100t\)
B\(I(t) = 2t e^{25t} \sin 100t\)
C\(I(t) = 2e^{25t} \cos 100t\)
D\(I(t) = 2t e^{25t} \cos 100t\)
Determine the inverse Laplace transform of \(\frac{1}{4s^2 - 8s}\)
A\(\frac{1}{4} e^t \sinh t\)
B\(\frac{1}{2} e^{2t} \sinh t\)
C\(\frac{1}{4} e^t \cosh t\)
D\(\frac{1}{2} e^{2t} \cosh t\)
Find the acute angle between the vectors \(z_1 = 3 - 4i\) and \(z_2 = -4 + 3i\).
A17°17′
B16°16′
C15°15′
D18°18′
Evaluate \(\Gamma\left(-\tfrac{3}{2}\right)\).
A\(\tfrac{2}{3}\sqrt{\pi}\)
B\(\tfrac{3}{4}\sqrt{\pi}\)
C\(\tfrac{1}{2}\sqrt{\pi}\)
D\(\tfrac{4}{3}\sqrt{\pi}\)
The cross product of vector A = 4i + 2j with vector B is 0. The dot product A·B = 30. Find B.
A6i + 3j
B6i − 3j
C3i + 6j
D3i − 6j