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Algebra of Complex Numbers

If z + 22+i...

Question

If $z + 2 (2 + i) = 8 + 9 i,$ then the value of $z$ is

4 + 7 i

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4 + 2 i

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7 - 3 i

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5 - 2 i

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Solution

The correct option is B $4 + 7 i$
Let $z = a + i b$
$z + 2 (2 + i) = 8 + 9 i z + 4 + 2 i = 8 + 9 i z = 4 + 7 i$

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