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MHT CET202415 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. B5 4
  3. C5 3
  4. D41 4

Correct answer

B. 5 4

Step-by-step solution

aligned & | z |+ z =2+ i & x^2+y^2 +x+ i y=2+ i aligned Equating real and imaginary parts, we get aligned & x^2+y^2 +x=2 and y=1 & x^2+1 =2-x & x^2+1=4-4 x+x^2 & 4 x=3 & x= 3 4 & z = 3 4 + i & |z|= ( 3 4 )^2+1^2 = 5 4 aligned

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