4.6 Complex Numbers

Notes

The imaginary unit is $\displaystyle i = \sqrt{-1}$, so $i^2 = -1$. A complex number has the form $a + bi$.

• $\displaystyle \sqrt{-25} = 5i$.
• Add or subtract the real and imaginary parts separately: $(3 + 2i) + (1 - 4i) = 4 - 2i$.
• Multiply like binomials and replace $i^2$ with $-1$: $(2 + i)(3 - i) = 6 - 2i + 3i - i^2 = 7 + i$.
• Equations with a negative discriminant have complex solutions: $x^2 + 9 = 0 \Rightarrow x = \pm 3i$.