Question

Find the center of the arc represented by $arg\frac{(z-3i)}{(z-2i+4)}=\pi /4$

• A. $9i-5$
• B. $\frac{1}{2}(9i-5)$
• C. $-9i+5$
• D. $\frac{1}{2}(-9i+5)$

Answer 1

The correct option is B $\frac{1}{2}(9i-5)$

If C is the center of the arc, then $\angle BCA=\pi /2$. Let C be $z_c$.
Then,
$\frac{z_c-3i}{z_c-2i+4}=e^{i\pi /2}=i$
$z_c=3i+i(z_c-2i+4)$
$=\frac{7i+2}{(1-i)}=\frac{1}{2}(9i-5)$
Ans: B