Question

Express
z=1/(-5-i) in standard (algebraic) form. Further, give an Argand diagram
in which z, z bar and −z are plotted.

Answer 1

Answer on Question #78432 – Math – Complex Analysis

Question

Express

$z = 1 / (-5 - i)$ in standard (algebraic) form. Further, give an Argand diagram in which $z$, $z$ bar and $-z$ are plotted.

Solution

$$z = \frac{1}{-5 - i} = -\frac{1}{5 + i} = -\frac{5 - i}{(5 + i)(5 - i)} = -\frac{5 - i}{25 + 1} = -\frac{5}{26} + \frac{1}{26}i.$$ $$-z = \frac{5}{26} - \frac{1}{26}i,$$ $$\bar{z} = -\frac{5}{26} - \frac{1}{26}i.$$

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