First slide

Algebra of complex numbers

Question

If $(4 + i) (z + \bar{z}) - (3 + i) (z - \bar{z}) + 26 i = 0,$ then the value of ${|z|}^{2}$ is

Moderate

A

13
B

17
C

19
D

11

Solution

Let $z = x + i y,$ then
$\begin{array}{lc} 2 (4 + i) x - (3 + i) 2 i y + 26 i = 0 \\ \Rightarrow & 4 x + y = 0, x - 3 y + 13 = 0 \\ \Rightarrow & x = - 1, y = 4 \\ ∴ & | z |^{2} = 17 \end{array}$

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