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NDA2023MathematicsComplex NumberActual

What is the value of 12+5 i + 12-5 i , where i= -1 ?

Options

  1. A24
  2. B25
  3. C5 2
  4. D5( 2 -1)

Correct answer

C. 5 2

Step-by-step solution

Let 12+5 i = x + iy 12+5 i =( x + iy )^2 x ^2- y ^2=12 ...(i) and 2 x y=5 ...(ii) On solving (i) and (ii), we get x= 5 2 , y= 1 2 So, 12+5 i = 5 2 + i 2 Similarly, 12-5 i = 5 2 - i 2 Now, 12+5 i + 12-5 i = 5 2 + i 2 + 5 2 - i 2 =5 2

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