Let z be a complex number such that the real part of is zero. Then, the maximum value of |z

Engineering

Mathematics

Geometry of Complex Number

Question

Let z be a complex number such that the real part of $\frac{z - 2 i}{z + 2 i}$ is zero. Then, the maximum value of |z –(6 + 8i)| is equal to

∞

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\frac{z - 2 i}{z + 2 i} + \frac{\bar{z} - 2 i}{\bar{z} + 2 i} = 0

\Rightarrow (z - 2 i) (\bar{z} - 2 i) + (z + 2 i) (\bar{z} + 2 i) = 0

\Rightarrow z \bar{z} - 2 i \bar{z} - 2 iz - 4 + z \bar{z} + 2 iz + 2 i \bar{z} - 4 = 0

\Rightarrow z \bar{z} = 4 \Rightarrow | z | = 2

max

| z - (6 + 8 i) | = 10 + 2 = 12

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