Q. Find the value of (1 + i)².
-
A.
2i
-
B.
2
-
C.
0
-
D.
1 + 2i
Solution
(1 + i)² = 1² + 2(1)(i) + i² = 1 + 2i - 1 = 2i.
Correct Answer: B — 2
Learn More →
Q. If z = 1 + i, find |z|².
Solution
|z|² = (1)² + (1)² = 1 + 1 = 2.
Correct Answer: B — 2
Learn More →
Q. If z = 1 + i, what is the value of z^3? (2023)
-
A.
-2 + 2i
-
B.
2i
-
C.
0
-
D.
2 + 2i
Solution
z^3 = (1 + i)^3 = 1 + 3i + 3i^2 + i^3 = 1 + 3i - 3 - i = -2 + 2i.
Correct Answer: A — -2 + 2i
Learn More →
Q. If z = 1 + i√3, find the conjugate of z.
-
A.
1 - i√3
-
B.
1 + i√3
-
C.
1 + √3i
-
D.
1 - √3i
Solution
The conjugate of a complex number z = a + bi is given by z* = a - bi. Thus, the conjugate of z = 1 + i√3 is 1 - i√3.
Correct Answer: A — 1 - i√3
Learn More →
Q. If z = 1 + i√3, what is the value of z^2? (2023)
-
A.
-2 + 2i√3
-
B.
4
-
C.
1 - 2i√3
-
D.
1 + 2i√3
Solution
z^2 = (1 + i√3)^2 = 1^2 + 2(1)(i√3) + (i√3)^2 = 1 + 2i√3 - 3 = -2 + 2i√3.
Correct Answer: A — -2 + 2i√3
Learn More →
Q. If z = 2 + 2i, find z².
-
A.
0
-
B.
8i
-
C.
8
-
D.
4 + 8i
Solution
z² = (2 + 2i)² = 4 + 8i - 4 = 8i.
Correct Answer: C — 8
Learn More →
Q. If z = 2 + 2i, what is the argument of z? (2023)
-
A.
π/4
-
B.
π/2
-
C.
3π/4
-
D.
0
Solution
The argument of z is given by tan^(-1)(2/2) = tan^(-1)(1) = π/4.
Correct Answer: A — π/4
Learn More →
Q. If z = 2(cos(π/3) + i sin(π/3)), what is z in rectangular form? (2022)
-
A.
1 + √3i
-
B.
2 + √3i
-
C.
1 + 2i
-
D.
2 + 2i
Solution
Using Euler's formula, z = 2(cos(π/3) + i sin(π/3)) = 2(1/2 + i√3/2) = 1 + √3i.
Correct Answer: A — 1 + √3i
Learn More →
Q. If z = 3 + 4i, what is the modulus of z? (2021)
Solution
The modulus of z is given by |z| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
Correct Answer: A — 5
Learn More →
Q. If z = 4 - 3i, find the conjugate of z. (2023)
-
A.
4 + 3i
-
B.
4 - 3i
-
C.
-4 + 3i
-
D.
-4 - 3i
Solution
The conjugate of z = 4 - 3i is z* = 4 + 3i.
Correct Answer: A — 4 + 3i
Learn More →
Q. If z = 5 + 12i, find the argument of z. (2020)
-
A.
arctan(12/5)
-
B.
arctan(5/12)
-
C.
π/2
-
D.
0
Solution
The argument of z = 5 + 12i is θ = arctan(12/5).
Correct Answer: A — arctan(12/5)
Learn More →
Q. If z1 = 2 + 2i and z2 = 2 - 2i, what is the value of z1 * z2? (2019)
Solution
z1 * z2 = (2 + 2i)(2 - 2i) = 4 - 4i^2 = 4 + 4 = 8.
Correct Answer: A — 8
Learn More →
Q. If z1 = 2 + 2i and z2 = 3 - i, find z1 + z2. (2023)
-
A.
5 + i
-
B.
5 + 3i
-
C.
1 + i
-
D.
1 - i
Solution
z1 + z2 = (2 + 2i) + (3 - i) = 5 + i.
Correct Answer: A — 5 + i
Learn More →
Q. What is the real part of the complex number z = -2 + 3i? (2020)
Solution
The real part of z is -2.
Correct Answer: A — -2
Learn More →
Q. What is the real part of the complex number z = 4 + 5i? (2022)
Solution
The real part of z = 4 + 5i is 4.
Correct Answer: A — 4
Learn More →
Q. Which of the following is the conjugate of the complex number z = 5 - 2i? (2021)
-
A.
5 + 2i
-
B.
5 - 2i
-
C.
-5 + 2i
-
D.
-5 - 2i
Solution
The conjugate of z = 5 - 2i is z* = 5 + 2i.
Correct Answer: A — 5 + 2i
Learn More →
Showing 1 to 16 of 16 (1 Pages)
