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MHT CET20242 May 2024Morning ShiftMathematicsComplex NumberActual

If a 0 and z = (1+ i )^2 a - i , i = -1 , has magnitude 2 5 , then z is equal to

Options

  1. A1 5 - 3 5 i
  2. B- 1 5 - 3 5 i
  3. C- 1 5 + 3 5 i
  4. D- 3 5 - 1 5 i

Correct answer

B. - 1 5 - 3 5 i

Step-by-step solution

aligned z & = (1+i)^2 a-i & = 2 i a-i & = 2 i(a+i) a^2+1 & = -2+2 a i a^2+1 |z| & = 4+4 a^2 (a^2+1 )^2 & 2 5 = 2 a^2+1 & a=3 aligned aligned & z= -2+2(3) i 3^2+1 = -2+6 i 10 & z= -1+3 i 5 & z = -1 5 - 3 i 5 aligned

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