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AP EAMCET202316 May 2023Morning ShiftMathematicsComplex NumberActual

If -3-4 i = re ^ i , then r ^2 =

Options

  1. A-5
  2. B5
  3. C10
  4. D-10

Correct answer

A. -5

Step-by-step solution

Given : -3-4 i =r e ...(i) Let -3-4 i =x+i y ...(ii) -3-4 i=(x+i y)^2=x^2-y^2+2 i x y Comparing both sides, x^2-y^2=-3 2 x y=-4 x y=-2 Solving above equations, we get x= 1 and y= 2 So, we have -3-4 i =(-1+2 i),(1-2 i) Now, -1+2 i=z₁ (Let) aligned & |z₁ |= 5 =r & (z₁ )= - ⁻¹ ( 2 1 )= - ⁻¹ 2 & = - ⁻¹ 2 & 2= ( - ) & - =2 =-2 aligned Now, r^2 =(5) (-2)=-10 .

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