In an Argand diagram, the point P represents the complex number z, where z = x + iy. Given that z + 2 = λi(z + 8), where λ is a real parameter, find the Cartesian equation of the locus of P as λ varies. If also z = μ(4 + 3i), where λ is real, prove that there is only one possible position for P

The answer is   "".

Explanation:

As the problem stands  

At the point of P, it is the complex number z in the Diagram of Argand and z = X+iy.  

We have said this:

where the parameter is a true  

The conceptual equation of the locus P varies between

And in equation mentioned above.

put the value of x, y  in equation (ii) we get:

to put the of in equation (iii) we get:

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