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Q1. What is the value of (1 + i)(1 - i)? (2019)
Solution:
(1 + i)(1 - i) = 1^2 - i^2 = 1 - (-1) = 1 + 1 = 2.
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Q2. If z = 5 + 12i, what is the imaginary part of z? (2022)
Solution:
The imaginary part of the complex number z = 5 + 12i is 12.
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Q3. If z = 1 + i, what is the value of z^2? (2022)
Solution:
z^2 = (1 + i)^2 = 1^2 + 2(1)(i) + i^2 = 1 + 2i - 1 = 2i.
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Q4. Find the real part of the complex number 4 + 5i. (2023)
Solution:
The real part of the complex number 4 + 5i is 4.
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Q5. What is the product of the complex numbers (1 + i) and (1 - i)? (2023) 2023
Solution:
(1 + i)(1 - i) = 1^2 - i^2 = 1 - (-1) = 2.
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Q6. If z = 2 - 3i, what is the conjugate of z? (2020)
Solution:
The conjugate of z = 2 - 3i is 2 + 3i.
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Q7. If z = 3 + 4i, what is the imaginary part of z? (2022) 2022
Solution:
The imaginary part of the complex number z = 3 + 4i is 4.
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Q8. If z = 3 + 4i, what is the value of z + z* (where z* is the conjugate of z)? (2017)
Solution:
z + z* = (3 + 4i) + (3 - 4i) = 6.
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Q9. What is the square root of the complex number -4? (2020)
Solution:
The square root of -4 is √(-1) * √4 = 2i.
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Q10. What is the value of (2 + 3i) / (1 + i)? (2015)
Solution:
Multiply numerator and denominator by the conjugate of the denominator: (2 + 3i)(1 - i) / (1 + i)(1 - i) = (2 - 2i + 3i + 3) / (1 + 1) = (5 + i) / 2 = 2.5 + 0.5i.
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