Anatomy of a Complex Number

A complex number has a Real part and an Imaginary part.

z =
Drag to sort
Real Part (a)
Imaginary Part (bi)

The Imaginary Unit

We define , which means .

Goal: Evaluate
1
-1
.
Tap to rotate

Perfect!

Adding Complex Numbers

Combine the Real parts together, and the Imaginary parts together.

Tap to combine like terms
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Multiplying Complex Numbers

When multiplying, you get an term. Remember: .

Tap the term to transform it Now tap like terms to combine them Fully simplified!
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🎉

Master of Complex Numbers!

You've successfully learned how to identify, rotate, add, and multiply complex numbers.

Key Takeaways:

  • (Real + Imaginary)
  • Combine like terms to add
  • Convert when multiplying