Complex number arithmetic

What you'll learn

1. 1

   Imagine a number that has two parts: a real part and an imaginary part. We write it as a + bi, where i is the square root of -1.

2. 2

   Drag the point on the complex plane to represent 3 + 2i (3 right, 2 up).

3. 3

   Let's add (2 + 3i) + (4 - i). We add real parts and imaginary parts separately.

4. 4

   What is (1 + 2i) + (3 + 4i)?

5. 5

   Now let's multiply (1 + 2i)(3 + 4i). Use FOIL — just like algebra, but remember i² = -1.

6. 6

   Try multiplying (2 + i)(1 - 3i) yourself. Type your answer as a + bi.

7. 7

   What is (2 + i)(1 - 3i)?