1.6 Complex Numbers
Ideas in this lesson
- Real and imaginary parts
- Adding and subtracting complex numbers
- Multiplying complex numbers
- Dividing complex numbers
- Powers of i
- Square roots of negative numbers
- Complex solutions of quadratic equations
- Complex conjugates
Real and imaginary parts · Worked example
If \((p-3)+(q+6)i=0\) with real p and q, what must p and q be?
Answer: \(p=3,\ q=-6\)
Equality of complex numbers requires equality of both real parts and imaginary parts.
\(p-3=0\) gives \(p=3\).
\(q+6=0\) gives \(q=-6\).
One equation involving p+q would not ensure both parts vanish.
\(p-3=0\) gives \(p=3\).
\(q+6=0\) gives \(q=-6\).
One equation involving p+q would not ensure both parts vanish.