Sum of amplitude of z and another complex number is π . other complex number can be written

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4-1.Complex numbers

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The sum of amplitude of $z$ and another complex number is $\pi $. The other complex number can be written

A

$\bar z$

B

$ - \overline z $

C

$z$

D

$ - z$

Solution

(b) We have $z = x + iy$ and let their complex ${z_2}$ and given that $arg\;(z) + {z_2} = \pi $
${z_2} = \pi – arg(z)$;

${z_2} = \pi + \left[ { – {{\tan }^{ – 1}}\frac{y}{x}} \right]$
${z_2} = \pi + [arg\;(\bar z)]$
which lies in second quadrant, i.e. $ – \bar z$.

Standard 11

Mathematics

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