Simplify \((3-i)^2 - 7(3-i) + 10\)
A-(3+i)
B3+i
C3-i
D-(3-i)
Mathematics · Question Bank
Advanced Engineering Mathematics
65 of 84 questions match · page 2 of 4. Answer in your head first, then check the solution.
What is \(4i^3\) times \(2i^2\)?
A-8i
B8i
C-8
D-8i^2
What is the quotient when \(4 + 8i\) is divided by \(i^3\)?
A8-4i
B8+4i
C-8+4i
D-8-4i
If \(A = -2 - 3i\) and \(B = 3 + 4i\), what is \(\frac{A}{B}\)?
A\(\frac{18-i}{25}\)
B\(\frac{-18-i}{25}\)
C\(\frac{-18+i}{25}\)
D\(\frac{18+i}{25}\)
Rationalize \(\frac{4+3i}{2-i}\)
A1+2i
B\(\frac{11+10i}{5}\)
C\(\frac{5+2i}{5}\)
D2+2i
What is the simplified expression of the complex number \(\frac{6+j2.5}{3+j4}\)?
A-0.32 + j0.66
B1.12 - j0.66
C0.32 - j0.66
D1.75 + j1.03
Perform the operation: \(4(\cos 60^\circ + i \sin 60^\circ)\) divided by \(2(\cos 30^\circ + i \sin 30^\circ)\) in rectangular coordinates.
A\(\sqrt{3} - 2i\)
B\(\sqrt{3} - i\)
C\(\sqrt{3} + i\)
D\(\sqrt{3} + 2i\)
Find the quotient of \(\frac{50+j35}{8+j5}\)
A\(6.47\angle 3^\circ\)
B\(4.47\angle 3^\circ\)
C\(7.47\angle 30^\circ\)
D\(2.47\angle 53^\circ\)
Evaluate \(\cosh(j\frac{\pi}{4})\)
A0.707
B1.41 + j0.866
C0.5 + j0.707
Dj0.707
Evaluate \(\tanh(j\frac{\pi}{3})\)
A0.5 + j1.732
Bj0.866
Cj1.732
D0.5 + j0.866
Evaluate the terms of a Fourier series \(2 e^{j10\pi t} + 2 e^{-j10\pi t}\) at \(t = 1\)
A2+j
B2
C4
D2+j2
Given the following series:
\(\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \dots\)
\(\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \dots\)
\(e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots\)
What relation can you draw from these series?
\(\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \dots\)
\(\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \dots\)
\(e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots\)
What relation can you draw from these series?
A\(e^x = \cos x + \sin x\)
B\(e^{ix} = \cos x + i \sin x\)
C\(e^{ix} = i \cos x + \sin x\)
D\(i e^x = i \cos x + i \sin x\)
One term of a Fourier series in cosine form is \(10 \cos 40\pi t\). Write it in exponential form.
A\(5 e^{j40\pi t}\)
B\(5 e^{j40\pi t} + 5 e^{-j40\pi t}\)
C\(10 e^{-j40\pi t}\)
D\(10 e^{j40\pi t}\)
Evaluate the determinant: \(\begin{vmatrix} 1 & 2 & 3 \\ -2 & -1 & -2 \\ 3 & 1 & 4 \end{vmatrix}\)
A4
B2
C5
D0
Evaluate the determinant: \(\begin{vmatrix} 1 & 6 & 0 \\ 4 & 2 & 7 \\ 0 & 5 & 3 \end{vmatrix}\)
A110
B-101
C101
D-110
If \(A = \begin{vmatrix} 2 & 3 & 1 \\ -1 & 2 & 4 \\ 0 & 5 & 7 \end{vmatrix}\), what is the cofactor of the second row, third column element?
A\(\begin{vmatrix} 2 & 3 \\ 0 & 5 \end{vmatrix}\)
B-\(\begin{vmatrix} 2 & 3 \\ 0 & 5 \end{vmatrix}\)
C-\(\begin{vmatrix} 1 & 7 \\ 2 & 0 \end{vmatrix}\)
D\(\begin{vmatrix} 3 & 1 \\ 5 & 7 \end{vmatrix}\)
If \(A = \begin{vmatrix} 3 & 1 & 2 \\ -2 & -1 & 0 \\ 0 & 2 & -1 \end{vmatrix}\), what is the cofactor of the first row, second column element?
A-\(\begin{vmatrix} 3 & 2 \\ 0 & -1 \end{vmatrix}\)
B\(\begin{vmatrix} -2 & -1 \\ 0 & 2 \end{vmatrix}\)
C\(\begin{vmatrix} 3 & 2 \\ 0 & -1 \end{vmatrix}\)
D-\(\begin{vmatrix} -2 & 0 \\ 0 & -1 \end{vmatrix}\)
If a \(3 \times 3\) matrix and its inverse are multiplied together, write the product.
A\(\begin{vmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{vmatrix}\)
B\(\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}\)
C\(\begin{vmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{vmatrix}\)
D\(\begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}\)
If matrix \(\begin{bmatrix} 1 & -1 & 2 \\ 2 & 1 & 3 \\ 0 & -1 & 1 \end{bmatrix}\) is multiplied by \(\begin{bmatrix} x \\ y \\ z \end{bmatrix}\) is equal to zero, then matrix \(\begin{bmatrix} x \\ y \\ z \end{bmatrix}\) is
A3
B1
C0
D-2
Given the matrix equation, solve for x and y:
\(\begin{bmatrix} 1 & 1 \\ 3 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 0 \end{bmatrix}\)
\(\begin{bmatrix} 1 & 1 \\ 3 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 0 \end{bmatrix}\)
A-4, 6
B-4, 2
C-4, -2
D-4, -6