If Re(\left( \frac{z - 8i}{z + 6} \right))= 0, then z lies o... | MATH - INTEGRAL POWER OF IOTA, ALGEBRAIC OPERATIONS AND EQUALITY OF COMPLEX NUMBERS | SolveeIt | Solveeit

Today, August 18

Question

If Re $\left( \frac{z - 8i}{z + 6} \right)$ = 0, then z lies on the curve -

A

4x – 3y + 24 = 0

B

x² + y² – 8 = 0

C

x² + y² + 6x – 8y = 0

D

None of these

Answer

x² + y² + 6x – 8y = 0

Explanation

Solution

Sol. Put z = x + iy

So, Re $\left( \frac{x + iy - 8i}{x + iy + 6} \right)$ = 0

Re $\left( \frac{\lbrack x + (y - 8)i\rbrack\lbrack x + 6 - iy\rbrack}{(x + 6)^{2} + y^{2}} \right)$ = 0

Ž x(x+6) + y(y–8) = 0

x² + y² + 6x – 8y = 0