Question

The solution of the equation $\frac{- 7 - 26i}{25}$.

• A. $\frac{- 7 + 26i}{25}$
• B. $\frac{7 + 26i}{25}$
• C. $(z + a)(\bar{z} + a)$
• D. $a$

Answer 1

Answer: (C)

$(z + a)(\bar{z} + a)$

Answer 2

$\left| \frac{3}{2} - 2i \right| - \left( \frac{3}{2} - 2i \right)$

Let $= \sqrt{\frac{9}{4} + 4} - \frac{3}{2} + 2i = \frac{5}{2} - \frac{3}{2} + 2i = 1 + 2i$, therefore $z_{1} = a + ib = (a,b)$

Equating real and imaginary parts, we get

$d > 0$and $|z_{1}| = |z_{2}|$⇒$a^{2} + b^{2} = c^{2} + d^{2}$

Hence complex number $\frac{z_{1} + z_{2}}{z_{1} - z_{2}} = \frac{(a + ib) + (c - id)}{(a + ib) - (c - id)}$.

Trick : Since $= \frac{\lbrack(a + c) + i(b - d)\rbrack\lbrack(a - c) - i(b + d)\rbrack}{\lbrack(a - c) + i(b + d)\rbrack\lbrack(a - c) - i(b + d)\rbrack}$

$= \frac{(a^{2} + b^{2}) - (c^{2} + d^{2}) - 2(ad + bc)i}{a^{2} + c^{2} - 2ac + b^{2} + d^{2} + 2bd}$.