If $(x + yi)(2 - i) = 5$, where $x$ and $y$ are real, find $x$ and $y$.

Question

Accepted Answer

$x = 2,\ y = 1$. $x + yi = \dfrac{5}{2 - i} = \dfrac{5(2 + i)}{(2 - i)(2 + i)} = \dfrac{5(2 + i)}{5} = 2 + i$, so $x = 2$ and $y = 1$. Check: $(2 + i)(2 - i) = 4 - i^2 = 5$. Using the wrong sign in the conjugate gives $2 - i$.

Answer

A) $x = 2,\ y = 1$

Answer

B) $x = 2,\ y = -1$

Answer

C) $x = 5,\ y = 0$

Answer

D) $x = 1,\ y = 2$

If $(x + yi)(2 - i) = 5$, where $x$ and $y$ are real, find $x$ and $y$.

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