Question

If $z\in C$ and ${log}_{|z+i|}|3+4i|<{log}_{|z+i|}|5+12i|$, then z lies

• A. Inside a circle passing through the origin
• B. Outside a circle passing through the origin
• C. Inside the disc
• D. Outside the curve z = - i +

Answer 1

The correct option is B Outside a circle passing through the origin

Let ${log}_{|z+1|}^5$ $<$ ${log}_{|z+1|}^{13}$ $\Rightarrow$ $|$z + 1$|$ $>$ 1
$\Rightarrow x^2+y^2+2y>0$