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Question

|z3|<1 and |z4i|>M then find the positive real value of M for which these exist at least one complex number z satisfy both the equation.

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Solution

|z3|<3 is the interior area of the circle having centre at (3,0) and radius 1.
Similarly, |z4i|>M is the exterior area of the circle of radius M and having centre at (0,4).

Distance between (3,0) and (0,4)=5

From the figure the value of M is =51=4
M=4 is the value for M for which there exists at least one complex number z satisfies both equations.

781088_707231_ans_0cb797546f7649fab3d480f3c292f9b2.png

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