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Q1. If z = 3 + 4i, what is the value of z + z̅? (2022)
Solution:
z + z̅ = (3 + 4i) + (3 - 4i) = 6.
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Q2. If z = 2 + 2i, what is |z|^2? (2021)
Solution:
|z|^2 = (2^2 + 2^2) = 4 + 4 = 8.
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Q3. If z = 3 + 4i, what is the value of |z|^2? (2019)
Solution:
|z|^2 = 3^2 + 4^2 = 9 + 16 = 25.
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Q4. 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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Q5. If z = 4 + 3i, what is the real part of z? (2023)
Solution:
The real part of the complex number z = 4 + 3i is 4.
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Q6. If z = 5 + 12i, what is the argument of z? (2022)
Solution:
The argument of z = 5 + 12i is given by arctan(12/5).
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Q7. 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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Q8. 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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Q9. 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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Q10. What is 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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