Q. What is the real part of the complex number z = 5e^(iπ/3)?
-
A.
5/2
-
B.
5/√3
-
C.
5√3/2
-
D.
5
Solution
The real part is Re(z) = 5cos(π/3) = 5 * 1/2 = 5/2.
Correct Answer: A — 5/2
Learn More →
Q. What is the sum of the complex numbers 2 + 3i and 4 - 5i?
-
A.
6 - 2i
-
B.
6 + 2i
-
C.
2 - 2i
-
D.
2 + 2i
Solution
The sum is (2 + 4) + (3 - 5)i = 6 - 2i.
Correct Answer: A — 6 - 2i
Learn More →
Q. What is the value of (1 + i)^2?
-
A.
2i
-
B.
2
-
C.
0
-
D.
1 + 2i
Solution
(1 + i)^2 = 1^2 + 2*1*i + i^2 = 1 + 2i - 1 = 2i.
Correct Answer: A — 2i
Learn More →
Q. What is the value of i^4?
Solution
i^4 = (i^2)^2 = (-1)^2 = 1.
Correct Answer: A — 1
Learn More →
Q. What is the value of z if z^2 = -1?
Solution
The solutions to z^2 = -1 are z = i and z = -i.
Correct Answer: A — i
Learn More →
Q. What is the value of |z| if z = -3 + 4i?
Solution
|z| = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5.
Correct Answer: A — 5
Learn More →
Q. What is the value of |z| if z = 4 - 3i?
Solution
|z| = √(4^2 + (-3)^2) = √(16 + 9) = √25 = 5.
Correct Answer: A — 5
Learn More →
Q. What is the value of |z| if z = 4e^(iπ/3)?
Solution
The modulus |z| = 4, as it is the coefficient in the polar form.
Correct Answer: A — 4
Learn More →
Q. What is the value of |z|^2 if z = 4 - 3i?
Solution
|z|^2 = 4^2 + (-3)^2 = 16 + 9 = 25.
Correct Answer: A — 25
Learn More →
Q. Which of the following is a purely imaginary number?
-
A.
2 + 3i
-
B.
0
-
C.
4
-
D.
0 + 5i
Solution
A purely imaginary number has no real part, so 0 + 5i is purely imaginary.
Correct Answer: D — 0 + 5i
Learn More →
Q. Which of the following is a root of the equation z^2 + 1 = 0?
Solution
The roots are z = ±i.
Correct Answer: A — i
Learn More →
Showing 91 to 101 of 101 (4 Pages)
