if |z|=2, then find the locus of complex number a+bz, where a,b are real numbers

Dear student,

Kindly find the answer to your query:

$$\begin{gathered} \left|\mathrm{z}\right|= 2 \\ \mathrm{Let} \mathrm{z} = \mathrm{x}+\mathrm{iy} \\ \sqrt{{\mathrm{x}}^2+{\mathrm{y}}^2}= 2 \\ {\mathrm{x}}^2+{\mathrm{y}}^2= 4 \\ \mathrm{Now} \\ \mathrm{Let} \mathrm{m} = \mathrm{a}+\mathrm{bz} \\ = \mathrm{a}+\mathrm{bx}+\mathrm{iby} \\ \mathrm{but} \mathrm{here} \mathrm{we} \mathrm{can} \mathrm{see} \mathrm{that} \mathrm{these} \mathrm{two} \mathrm{equation} \mathrm{are} \mathrm{not} \mathrm{co} \mathrm{related} \mathrm{so} \mathrm{kindly} \mathrm{recheck} \mathrm{the} \\ \mathrm{question}. \\ \mathrm{Regards} \end{gathered}$$
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