Topic: Complex numbers

Levels Supported

Primary: no

Junior: no

Intermediate: yes

Senior: yes

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Intermediate

Complex numbers extend the real numbers by introducing a new number, $i$, defined by $i^2 = -1$. Every complex number can be written as $a + bi$, where $a$ and $b$ are real numbers. Here, $a$ is called the real part and $b$ is the imaginary part.

Important properties:

• Addition and subtraction: $(a + bi) + (c + di) = (a + c) + (b + d)i$

• Multiplication: $(a + bi)(c + di) = (ac - bd) + (ad + bc)i$

• The conjugate of $a + bi$ is $a - bi$

• The modulus (absolute value) of $a + bi$ is $|a + bi| = \sqrt{a^2 + b^2}$

• Complex numbers can be plotted on the complex plane, with the horizontal axis for the real part and the vertical axis for the imaginary part

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Validation

Mathematical correctness: OK Age suitability: OK Progression between levels: OK