Question

Equation of tangent drawn to circle |z| = r at the point A (z₀) is

• A. R_e$\left( \frac{z}{z_{0}} \right)$ = 1
• B. R_e$\left( \frac{z_{0}}{z} \right)$ = 1
• C. Im $\left( \frac{z}{z_{0}} \right)$ = 1
• D. Im $\left( \frac{z_{0}}{z} \right)$ = 1

Answer 1

Answer: (A)

R_e$\left( \frac{z}{z_{0}} \right)$ = 1

Answer 2

Sol. $\frac{z - z_{0}}{z_{0}}$ is purely imaginary

$\frac{z - z_{0}}{z_{0}} + \frac{\bar{z} - {\bar{z}}_{0}}{{\bar{z}}_{0}}$ = 0

Ž $\frac{z}{z_{0}} + \overline{\left( \frac{z}{z_{0}} \right)}$ = 2

Ž 2R_e $\left( \frac{z}{z_{0}} \right)$ = 2

Ž R_e $\left( \frac{z}{z_{0}} \right)$ = 1