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MHT CET202411 May 2024Morning ShiftMathematicsComplex NumberActual

Let Z be a complex number such that |Z|+Z=2+i( where i= -1 ) , then |Z| is equal to

Options

  1. A4 5
  2. B41 4
  3. C5 3
  4. D5 4

Correct answer

D. 5 4

Step-by-step solution

array ll & Let z=a+i b & |z|= a^2+b^2 & |z|+z=2+i & a^2+b^2 +a+i b=2+i array Comparing both sides, we get a^2+b^2 +a=2 and b=1 array ll & 1+a^2 +a=2 & 1+a^2=(2-a)^2 & 1+a^2=4-4 a+a^2 & 4 a=3 array array ll & a= 3 4 & |z|= a^2+b^2 = 5 4 array

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