How many solutions the system of equations `||z + 4 |-|z-3i|| =5` and |z| = 4 ` has ?

Explanation

To solve the system of equations given by \( ||z + 4| - |z - 3i|| = 5 \) and \( |z| = 4 \), we will analyze each equation step by step.

### Step 1: Understanding the equations

The first equation is \( ||z + 4| - |z - 3i|| = 5 \). This represents the absolute difference between the distance of the complex number \( z \) from the point \( -4 \) and the point \( 3i \).

The second equation \( |z| = 4 \) represents a circle in the complex plane with a center at the origin (0,0) and a radius of 4.

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