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