ACT Math — Number and Quantity — Drill 3

About This Drill

ACT Math — Number and Quantity — Drill 3 is a Math practice drill covering Number and Quantity. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

This advanced ACT Number and Quantity drill focuses on the most challenging topics in the category: performing arithmetic with complex numbers, working with powers of the imaginary unit i, and performing vector operations including computing magnitude and applying scalar multiplication.

Questions in This Drill

1. Given i = √−1, what is (5 + 3i) + (2 − 7i)?
2. Given i = √−1, what is (3 + 2i)(1 − 4i)?
3. Vector u has components ⟨3, 4⟩ and vector v has components ⟨−1, 2⟩. What is the magnitude of u + v?
4. Given i = √−1, what is the value of i⁴³?
5. Vector w has components ⟨−2, 5⟩. What are the components of the vector 3w − ⟨1, 1⟩?