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Question

Let z=x+iy be a complex number satisfying equation |z(2+i)|=|Re(z)4|
Which of the following options describes the above equation ? 
  1. y=1±23x
  2. y=2±3x
  3. y=1±32x
  4. y=3±2x


Solution

The correct option is A y=1±23x
z=x+iy|z(2+i)|=|Re(z)4||x2+i(y1)|=|x4|(x2)2+(y1)2=(x4)2(y1)2=(x4)2(x2)2
(y1)2=2(2x6)y=1±23x

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