Number Types & Properties

Complex Number

2. What is the sum of the complex numbers 3 – 4i and 5 + 3i?

2018 April(A09) Math Question 2

For the complex variable z, one of the following is a solution of z² = −9. Which one?

2025 October(J08) Math Question 10

Which of the following numbers is equal to (10i + 2)/(2i)? (Note: i² = −1)

2025 October(J08) Math Question 15

Which of the following is a possible sum of the complex numbers √(−9) and √(−16)?

2023 September(G01) Math Question 15

20. One of the following values for a makes the expression (2a+5)/(a2+1) undefined. Which one?

Undefined fraction

2021 April(D05) Math Question 20

Let z = 4 + 5i and w = 3 + 7i, where i is the imaginary unit. What is the value of 2z + w?

2024 June(G20) Math Question 22

Which of the following is the complex conjugate of 2 + 7i?

2024 April(Z13) Math Question 27

2018 December(B05) Math Question 29

32. What is the complex conjugate of the number below?

Division of imaginary numbers (the use of conjugates)

2021 April(D05) Math Question 32

Given i² = −1, −2i(3 + 4i) − 3(2 + 5i) = ?

2024 September(H11) Math Question 34

36. Given that i is the imaginary unit, which of the following complex numbers is equal to (7 + 6i)2 ?

2020 December(D03) Math Question 36

Given i² = −1, which of the following expressions is equivalent to (9i − 2)(3 − 5i)?

2024 December(H31) Math Question 36

2011 June(69F) Math Question 41

2009 April(66F) Math Question 41

What are all the values of z that make the equation below true? z² + z + 3 = 0

2024 December(H31) Math Question 42

43. For i = square root of -1, (1 + 2i)^2 = ?

2016 April(73E) Math Question 43

2021 June(D06) Math Question 44

What are the solutions of (x + 1)² + 1 = 0?

2024 September(H11) Math Question 45

For √(−1) = i, and for certain real numbers a and b, the equation (10 − i) + (8 + 6i) = a + bi is true. What is the value of ab?

2024 December(H31) Math Question 47

2012 June(70C) Math Question 51

35 February(Z14) Math Question 51

53. The product of 2 numbers is 25. If 1 of the numbers is the complex number 4 + 3i, what is the other number?

2014 April(71H) Math Question 53

53. Given that b is rational and i = √••−1 , the product of the expression (3 + bi) and which of the following expressions must be a rational number?

2021 December(E23) Math Question 53

2013 April(71G) Math Question 54

2021 April(Z04) Math Question 55

Which of the following numbers is a solution to the equation 3x² + x + 5 = 0?

2023 April(F11) Math Question 55

2020 June(C02) Math Question 56

57. What is the distance, in coordinate units, between 2 + 6i and —4 + 3i in the complex plane?

2016 December(74H) Math Question 57

58. Karie is inventing a new notation in math. She has decided to use n.L to denote the sum of the first a positive integers. For example, 51 means 5 + 4 + 3 + 2 + 1. Karie has written 3 statements that she is investigating as possible properties of

2018 April(A09) Math Question 58

58. For all real numbers x and the imaginary number i, which of the following expressions is equivalent to

2017 June(74C) Math Question 58

58. Given a positive integer n such that i^n = 1, which of the following statements about n must be true? (Note: i² = – 1)

Complex NumberNumber Types & PropertiesACT math questions

2018 April(A09) Math Question 2

2025 October(J08) Math Question 10