Q. What is the value of (2 + 3i)(2 - 3i)? (2019)
Solution
Using the difference of squares: (a + b)(a - b) = a² - b². Here, (2)² - (3i)² = 4 - (-9) = 4 + 9 = 13.
Correct Answer:
A
— 13
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Q. What is the value of (3 + 4i) / (1 + i)? (2021)
-
A.
2 + i
-
B.
1 + 2i
-
C.
3 - 4i
-
D.
1 - i
Solution
Multiplying numerator and denominator by the conjugate of the denominator: (3 + 4i)(1 - i) / (1 + i)(1 - i) = (3 - 3i + 4i + 4) / 2 = (7 + i) / 2 = 2 + i.
Correct Answer:
A
— 2 + i
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Q. Which of the following is the conjugate of the complex number 2 - 3i? (2020)
-
A.
2 + 3i
-
B.
2 - 3i
-
C.
3 - 2i
-
D.
3 + 2i
Solution
The conjugate of a complex number a + bi is a - bi. Thus, the conjugate of 2 - 3i is 2 + 3i.
Correct Answer:
A
— 2 + 3i
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Q. Which of the following is the conjugate of the complex number 5 - 3i? (2020)
-
A.
5 + 3i
-
B.
5 - 3i
-
C.
-5 + 3i
-
D.
-5 - 3i
Solution
The conjugate of a complex number a + bi is a - bi. Thus, the conjugate of 5 - 3i is 5 + 3i.
Correct Answer:
A
— 5 + 3i
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