Complex Numbers

⏱ Time: 0s

Q1. Which of the following is the conjugate of the complex number 5 - 3i? (2020)

Solution:

The conjugate of a complex number a + bi is a - bi. Thus, the conjugate of 5 - 3i is 5 + 3i.

⏱ Time: 0s

Q2. What is the square root of the complex number -1? (2021)

Solution:

The square root of -1 is defined as i.

⏱ Time: 0s

Q3. If z = 1 + √3i, what is the argument of z? (2015)

Solution:

The argument is given by tan^(-1)(√3/1) = π/3.

⏱ Time: 0s

Q4. 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.

⏱ Time: 0s

Q5. 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.

⏱ Time: 0s

Q6. What is the sum of the complex numbers 3 + 2i and 1 - 4i? (2023)

Solution:

(3 + 2i) + (1 - 4i) = (3 + 1) + (2 - 4)i = 4 - 2i.

⏱ Time: 0s

Q7. Find the real part of the complex number 4 + 5i. (2023)

Solution:

The real part of the complex number 4 + 5i is 4.

⏱ Time: 0s

Q8. 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.

⏱ Time: 0s

Q9. What is the product of the complex numbers 2 + 3i and 4 - i? (2021)

Solution:

(2 + 3i)(4 - i) = 8 - 2i + 12i - 3i^2 = 8 + 10i + 3 = 11 + 10i.

⏱ Time: 0s

Q10. What is the argument of the complex number -1 + 0i? (2021)

Solution:

The argument of -1 + 0i is π (180 degrees) since it lies on the negative x-axis.