Complex Arithmetic/Examples/z 1^2 + 2 z 1 - 3
Jump to navigation
Jump to search
Example of Complex Arithmetic
Let $z_1 = 1 - i$.
Then:
- ${z_1}^2 + 2 z_1 - 3 = -1 - 4 i$
Proof
\(\ds {z_1}^2 + 2 z_1 - 3\) | \(=\) | \(\ds \paren {1 - i}^2 + 2 \paren {1 - i} - 3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {1 - 2 i + i^2} + \paren {2 - 2 i} - 3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds -2 i + 2 - 2 i - 3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds -1 - 4 i\) |
$\blacksquare$
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Fundamental Operations with Complex Numbers: $54 \ \text {(a)}$