Simplify the expression \(i^{1997} + i^{1999}\), where i is an imaginary number.
A0
B-i
C1+i
D1-i
Mathematics · Question Bank
Advanced Engineering Mathematics
40 of 84 questions match · page 1 of 2. Answer in your head first, then check the solution.
Simplify: \(i^{29} + i^{21} + i\)
A3i
B1-i
C1+i
D2i
Write in the form \(a+bi\) the expression \(i^{3217} - i^{427} + i^{18}\)
A2i+1
B-i+1
C2i-1
D1+i
The expression \(3+4i\) is a complex number. Compute its absolute value.
A4
B5
C6
D7
Write the polar form of the vector \(3 + j4\)
A\(6\angle 53.1^\circ\)
B\(10\angle 53.1^\circ\)
C\(5\angle 53.1^\circ\)
D\(8\angle 53.1^\circ\)
Evaluate the value of \(\sqrt{-10} \times \sqrt{-7}\)
Ai
B-\sqrt{70}
C\sqrt{70}
D\sqrt{17}
Simplify \((3-i)^2 - 7(3-i) + 10\)
A-(3+i)
B3+i
C3-i
D-(3-i)
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
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