Complex Arithmetic
Add, multiply and divide using i² = −1 and conjugates.
Key idea
Add, multiply and divide using i² = −1 and conjugates.
In depth
Add or subtract real and imaginary parts separately. Multiply with distribution and replace i² with −1. Divide by multiplying top and bottom by the conjugate.
Worked example
(2 + 3i)(1 − i) = 2 − 2i + 3i − 3i² = 5 + i.
Formula
Real-world uses
- Calculating impedance in electrical engineering
- Combining wave signals in communications
Common mistake
Forgetting i² = −1 and leaving i² in the answer.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Complex Arithmetic?
Add, multiply and divide using i² = −1 and conjugates. It is a topic at the advanced level in Algebra.
What is the formula for Complex Arithmetic?
The key formula is (a+bi)(c+di).
Where is Complex Arithmetic used in real life?
Real-world examples: Calculating impedance in electrical engineering; Combining wave signals in communications.
What should I learn before Complex Arithmetic?
Make sure you are comfortable with Complex Numbers, the previous topic in Algebra.
What is a common mistake with Complex Arithmetic?
Forgetting i² = −1 and leaving i² in the answer.
How can I practise Complex Arithmetic?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Complex Arithmetic?
Move on to Complex Conjugates next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.