First slide

Algebra of complex numbers

Question

If $\bar{z} = 3 i + \frac{25}{z + 3 i}$ then $| z |$ cannot exceed

Moderate

A

3
B

8
C

16
D

18

Solution

$(\bar{z} - 3 i) (z + 3 i) = 25$
$\Rightarrow | z - 3 i |^{2} = 25 or | z - 3 i | = 5$
Now, $\begin{array}{l} | z | = | (z - 3 i) + 3 i | \\ \leq | z - 3 i | + | 3 i | = 5 + 3 = 8 \end{array}$

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