Question

If $\frac {2z_1} {3z_2}$ is a purely imaginary number, then $|\frac {z_1-z_2} {z_1+z_2}|$ is equal to

• A. $\frac {3} {2}$
• B. 1
• C. $\frac {2} {3}$
• D. $\frac {4} {9}$

Answer 1

Answer: (B)

1

Answer 2

Let $\frac{2z_{1}}{3z_{2}}=id$ $\therefore \left|\frac{z_{1}-z_{2}}{z_{1}+z_{2}}\right|=\left|\frac{\frac{z_{1}}{z_{2}}-1}{\frac{z_{1}}{z_{2}}-1}\right|$ $=\left|\frac{\frac{3ki}{2}-1}{\frac{3ki}{2}+1}\right|$ $=\left|\frac{3ki-2}{3ki+2}\right|=1$