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How many solutions the system of equa...

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

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`||z+4|-|z-3i||=5`
`||z+4|-|z-3i||=|4+3i|`
This represents two rays emanating from '-4' and '3i' and moving in opposite directions.
`|z|=4` represents a circle having centre at origin and radius '4'.

Clearly, curves interesect at two points, A and B.
Hence, system of equations has two solutions.
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