If z - x - iy then the value of z - z-z - z- is

The correct option is D iy/x Given, z=x+iy ∴ z z̅ #160; / z+z̅ #160; =( x+iy x+iy / x+iy+x iy ) 2iy / 2x = iy x ...

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Byju's Answer

Standard XII

Mathematics

Properties of Conjugate of a Complex Number

If z = x + ...

Question

If $z = x + i y$ then the value of $\frac{z - ¯ z}{z + ¯ z}$ is

\frac{y}{i x}

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- \frac{i x}{y}

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\frac{i x}{y}

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\frac{i y}{x}

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Solution

The correct option is D $\frac{i y}{x}$
Given, $z = x + i y$
$∴ \frac{z - ¯ z}{z + ¯ z} = (\frac{x + i y - x + i y}{x + i y + x - i y}) \frac{2 i y}{2 x}$
$= \frac{i y}{x}$

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If z=x+iy then the value of z−¯zz+¯z is

The correct option is D iyxGiven,z=x+iy∴z−¯zz+¯z=(x+iy−x+iyx+iy+x−iy)2iy2x=iyx

If $z = x + i y$ then the value of $\frac{z - ¯ z}{z + ¯ z}$ is

The correct option is D $\frac{i y}{x}$
Given, $z = x + i y$
$∴ \frac{z - ¯ z}{z + ¯ z} = (\frac{x + i y - x + i y}{x + i y + x - i y}) \frac{2 i y}{2 x}$
$= \frac{i y}{x}$