Complex numbers by hand

Add, multiply and divide with i² = −1, then find modulus and argument. About 9 minutes, A-level.

What you will do

1. A number with an imaginary part. A complex number is a + bi where i^2 = -1. Treat i like a letter, with that one special rule.
2. Adding. Add the real parts together and the imaginary parts together.
3. Multiplying. Expand like brackets, then replace i^2 by -1.
4. Dividing. Multiply top and bottom by the conjugate of the bottom so that the denominator becomes real.
5. Modulus and argument. The modulus is the distance from the origin and the argument is the angle.