Complex Subtraction/Examples/(8 - 6i) - (2i - 7)

Example of Complex Subtraction

$\paren {8 - 6 i} - \paren {2 i - 7} = 15 - 8 i$

Proof

\(\ds \paren {8 - 6 i} - \paren {2 i - 7}\)

\(=\)

\(\ds \paren {8 + \paren {-6 i} } + \paren {-\paren {-7 + 2 i} }\)

Definition of Complex Subtraction

\(\ds \)

\(=\)

\(\ds \paren {8 + \paren {-\paren {-7} } } + \paren {\paren {-6} + {\paren {-2} } } i\)

Definition of Complex Addition

\(\ds \)

\(=\)

\(\ds \paren {8 + 7} + \paren {-6 - 2} i\)

\(\ds \)

\(=\)

\(\ds 15 - 8 i\)

$\blacksquare$

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Solved Problems: Fundamental Operations with Complex Numbers: $1 \ \text {(c)}$