Choose “Save as PDF” in the print dialog to keep a copy.

Cogito

Algebra 2 · Chapter 2 · Lesson 2

Practice Worksheet

Arithmetic with Complex Numbers

Treat i like a letter, then replace i squared.

11 problems · about 23 minutes · N-CN.A.2

NameDate

Figure — use these to answer the problems

A complex number is a point on a plane. Adding them adds components.

Vector a(3, 2)
Vector b(1, 4)
a + b(4, 6)

Real part of the first3

Imaginary part of the first2

Real part of the second1

Imaginary part of the second4

Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

(4 + 3i)(4 − 3i). Result?
Answer
(1 + i) + (5 + 3i). Imaginary part?
Answer
(6 + 2i) − (2 + 5i). Real part?
Answer
What is i⁴?
Answer

Build It Up

The same ideas with more to keep track of.

3 problems

(2 + i)(2 − i). What is the result? It is real.
Answer
Conjugate of 3 + 7i. What is its imaginary part?
Answer
(1 + 2i)(1 − 2i). Result?
Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

8
Order the steps for dividing by a complex number.
Write 1 to 4 in the boxes to put these in order.
- Find the conjugate of the denominator
- Multiply top and bottom by it
- Replace every i squared with −1
- Split into real and imaginary parts
Is 5 a complex number? 1 for yes, 0 for no.
Answer
Adding
(3 + 2i) + (4 + 5i). What is the real part?
Answer
The Square
What is i²?
Answer