The correct option is D zz=25 Given, #160; z = 3 4i So, z̅ = 3+4i z z̅ = 8i 1 z = 3+4i 25 #160; z ^ 2 = 7 24i zz̅ ...

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Properties of Conjugate of a Complex Number

If z=3-4i, ...

Question

If $z = 3 - 4 i$ , then

z - ¯ ¯ ¯ z = - 8

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\frac{1}{z} = ¯ ¯ ¯ z

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z^{2} = + 7 - 24 i

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z ¯ ¯ ¯ z = 25

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Solution

The correct option is D $z ¯ ¯ ¯ z = 25$
Given, $z = 3 - 4 i$

So, $¯ z = 3 + 4 i$

$z - ¯ z = - 8 i$

$\frac{1}{z} = \frac{3 + 4 i}{25}$

$z^{2} = - 7 - 24 i$

$z ¯ z = (3 - 4 i) (3 + 4 i) = 9 - 12 i + 12 i + 16 = 25$

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