InterviewSolution
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InterviewSolution
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Find the square root `9+40 idot` |
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Answer» Correct Answer - `(5+4i) or - (5+4i)` Let `sqrt(9+40i) = x +iy`. Then `(x + iy)^(2) = 9+40i` `or x^(2) - y^(2) = 9" "(1)` `and xy = 20" "(2)` Squaring (1) and adding with 4 times the square of (2), we get `x^(4) + y^(4) - 2x^(2)y^(2)+ 4x^(2)y^(2) = 81 + 1600` `or (x^(2) +y^(2))= 1681` or `x^(2) + y^(2) = 41" "(3)` From`(1) +(3)`, we get `x^(2)= 25 or x = pm 5` and `y =pm4` From Eq. (2) we can see that x and y are of same sign. Therefore, `x+iy= (5+4i) or - (5+41)` |
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