Complex Algebra/Examples/3x + 2iy - ix + 5y = 7 + 5i
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Example of Complex Algebra
Let $3 x + 2 i y - i x + 5 y = 7 + 5 i$.
Then:
\(\ds x\) | \(=\) | \(\ds -1\) | ||||||||||||
\(\ds y\) | \(=\) | \(\ds 2\) |
Proof
\(\ds 3 x + 2 i y - i x + 5 y\) | \(=\) | \(\ds 7 + 5 i\) | ||||||||||||
\(\ds \leadsto \ \ \) | \(\ds \paren {3 x + 5 y} + \paren {2 y - x} i\) | \(=\) | \(\ds 7 + 5 i\) | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds 3 x + 5 y\) | \(=\) | \(\ds 7\) | |||||||||||
\(\ds 2 y - x\) | \(=\) | \(\ds 5\) | ||||||||||||
\(\ds \leadsto \ \ \) | \(\ds x\) | \(=\) | \(\ds -1\) | |||||||||||
\(\ds y\) | \(=\) | \(\ds 2\) |
$\blacksquare$
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: $3$