Complex Numbers | Visualize & Solve with De Moivre’s Theorem
Understanding complex numbers opens the door to solving problems that regular numbers can’t handle. This solver breaks everything down into friendly, digestible lessons to help you grasp new ideas at your own pace.
\(z^n = r^n \left( \cos(n\theta) + i \sin(n\theta) \right)\)
Complex numbers are made up of two parts: a real part and an imaginary part (involving the square root of -1, written as i). Though they may sound “complicated,” they’re just another way to represent numbers—especially useful in physics, engineering, and advanced math.
What You’ll Learn:
- How to write and understand complex numbers in Cartesian form
- Plotting points on an Argand Diagram
- Performing basic operations: addition, subtraction, multiplication, and division
- Solving complex equations
- Converting complex numbers to polar form
- Real-world applications of complex numbers
Once you’re comfortable with complex numbers, you’re ready to level up with De Moivre’s Theorem. This powerful formula helps you raise complex numbers to powers and find roots, especially in polar form.
In This Module:
- What De Moivre’s Theorem is and how to apply it
- Using it to solve powers and roots of complex numbers
- Converting to exponential form for smoother calculations
- A first look at locus problems, where you’ll explore how complex numbers move and behave
This section links together previous modules to help you connect the dots. You’ll find familiar ideas from trigonometry, polar coordinates, and roots & indices.