2.4 Operations with Complex Numbers

Notes

Treat $i$ like a variable, then replace $i^2$ with $-1$.

• Add/subtract: combine real parts and imaginary parts. $(2 + 5i) + (1 - 3i) = 3 + 2i$.
• Multiply: FOIL. $(1 + 2i)(3 - i) = 3 - i + 6i - 2i^2 = 3 + 5i + 2 = 5 + 5i$.
• The complex conjugate of $a + bi$ is $a - bi$, and $(a + bi)(a - bi) = a^2 + b^2$.
• Divide: multiply top and bottom by the conjugate of the denominator.