Complex Numbers
Work with imaginary and complex numbers and the complex plane.
The Square Root of -1
Imaginary Numbers
Complex Numbers
Plotting Complex Numbers
Identifying Complex Points
Combining Complex Numbers
Adding Complex Numbers
Subtracting Complex Numbers
Absolute Value
Complex Separation
Scalar Multiplication
Scaling Magnitudes
Simplifying Expressions
Multiplying by i
Rotation by Multiplication
Multiple Rotations
Scaling and Rotating
General Multiplication
Course description
In this course you'll understand how complex numbers arise naturally as solutions to equations. You'll learn to manipulate them according to the usual rules of algebra and derive geometric insights from the complex plane.
Topics covered
- Complex numbers as solutions to quadratic equations.
- Addition and subtraction of complex numbers.
- Absolute value and scaling of complex numbers.
- Multiplying complex numbers algebraically.
- The geometric interpretation of complex multiplication.
- Complex conjugates.
- Dividing complex numbers.
- Complex numbers in polar form.
- Powers and roots.
Prerequisites and next steps
Assumes comfort with the cartesian and polar coordinate plane, quadratic equations and basic trigonometry.