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
56 of 84 questions match · page 1 of 3. 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)
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\(33.4\angle 45^\circ\)
What is \(4i^3\) times \(2i^2\)?
A-8i
B8i
C-8
D-8i^2
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
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
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\(\frac{-90+220i}{169}\)
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\(2.47\angle 53^\circ\)
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