Q. What is the value of (2 + 3i) + (4 - 2i)?
A.
6 + i
B.
6 + i
C.
2 + 5i
D.
8 + i
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Solution
To add the complex numbers, we combine the real parts and the imaginary parts: (2 + 4) + (3 - 2)i = 6 + 1i = 6 + i.
Correct Answer:
A
— 6 + i
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Q. What is the value of |z| if z = -1 - i?
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Solution
The modulus |z| = √((-1)² + (-1)²) = √(1 + 1) = √2.
Correct Answer:
A
— √2
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Q. Which of the following complex numbers lies on the unit circle?
A.
1 + 0i
B.
0 + 1i
C.
1 + 1i
D.
0 + 0i
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Solution
A complex number z lies on the unit circle if |z| = 1. For z = 1 + 0i, |z| = √(1² + 0²) = 1. For z = 0 + 1i, |z| = √(0² + 1²) = 1. Both 1 + 0i and 0 + 1i lie on the unit circle.
Correct Answer:
A
— 1 + 0i
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Q. Which of the following is the conjugate of the complex number z = 2 - 3i?
A.
2 + 3i
B.
2 - 3i
C.
3 - 2i
D.
3 + 2i
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Solution
The conjugate of a complex number z = a + bi is given by z* = a - bi. Here, the conjugate is 2 + 3i.
Correct Answer:
A
— 2 + 3i
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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
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Solution
The conjugate of z = 5 - 2i is z* = 5 + 2i.
Correct Answer:
A
— 5 + 2i
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Q. Which of the following is the conjugate of the complex number z = 5 - 3i?
A.
5 + 3i
B.
5 - 3i
C.
3 - 5i
D.
3 + 5i
Show solution
Solution
The conjugate of a complex number z = a + bi is given by z* = a - bi. Here, the conjugate of 5 - 3i is 5 + 3i.
Correct Answer:
A
— 5 + 3i
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Q. Which of the following represents the complex number 4 in polar form?
A.
4(cos 0 + i sin 0)
B.
4(cos π/2 + i sin π/2)
C.
4(cos π + i sin π)
D.
4(cos π/4 + i sin π/4)
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Solution
The polar form of a complex number r(cos θ + i sin θ) where r is the modulus and θ is the argument. Here, 4 = 4(cos 0 + i sin 0).
Correct Answer:
A
— 4(cos 0 + i sin 0)
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