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AP EAMCET202317 May 2023Morning ShiftMathematicsComplex NumberActual

For real numbers a and b , if 4 a+i(3 a-b)=b-6 i and z=a+ b 4 i , then |z| a =

Options

  1. A2 2
  2. B6 2
  3. C2
  4. D2

Correct answer

C. 2

Step-by-step solution

4 a+i(3 a-b)=b-6 i Comparing both sides, we get : aligned & 4 a=b & 3 a-b=-6 3 a-4 a=-6 , a=6 & b=24 & Z=a+ b 4 i z=6+ 24 4 i=6+6 i & |z|= 36+36 =6 2 & |z| a = 6 2 6 = 2 aligned

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