If $z$ is a complex number satisfying the equation $|z+i|+|z−i|=8 $ then maximum value of $|z|$ is ?
I took $z$ as a point p on the graph and drew lines connecting it to $i$ and $-i$. I assumed $z=x+iy$. Therefore x and y should be maximum. If x and y are maximum, the triangle by i,-i and z has maximum area i.e. height is maximum. Taking i and -i as the base, max height come out when z is on the x axis at distance √15 from origin. But the answer is 4. Please solve it.