Virginia SOL Math / Algebra II / Expressions & Operations
Operate With Complex Numbers
What you'll learn
- Simplify powers of i and square roots of negatives
- Add, subtract, and multiply complex numbers
- Plot a complex number on the complex plane
Words to know
- Imaginary unit i —
- the number with i^2 = -1
- Complex number —
- a number of the form a + bi
- Real part —
- the value a in a + bi
- Imaginary part —
- the value b in a + bi
- Complex plane —
- a grid with real and imaginary axes
Why it matters Complex numbers let every quadratic have solutions and are used in engineering and physics to model waves and circuits.
Worked examples
Model ItI do
Plot 3 + 2i and simplify sqrt(-16).
For 3 + 2i, move 3 right on the real axis and 2 up on the imaginary axis, and mark the point. For sqrt(-16), write it as sqrt(16) * sqrt(-1) = 4i.
Try It TogetherWe do
Simplify (3 + 2i) + (1 - 5i).
Add real parts and imaginary parts separately: (3 + 1) + (2 - 5)i = 4 - 3i.
Now YouYou do
Simplify (4 + i)(2 - i).
Use FOIL and replace i^2 with -1. Check your answer in the back of this chapter.
Practice
Mastered 0 of 11
Warm-up
Ease in with the basics.
1.Simplify sqrt(-49).
2.Add (4 + 2i) + (3 + 5i).
3.Simplify i^3.
On Level
The core Quick Check from the book.
1.Simplify sqrt(-25).
2.Simplify i^2.
3.Add (2 + 3i) + (5 - i).
4.Subtract (6 + 2i) - (1 + 4i).
5.Multiply (1 + i)(1 - i).
Challenge
Stretch your thinking.
1.Multiply (3 + 2i)(4 - i).
2.Simplify (2 - 3i)^2.
3.Multiply (5 + 3i)(5 - 3i).