COMEDK 2025 Afternoon Solved Paper

Concept:Simplify the complex number to $a+ib$ form and identify the quadrant based on signs of $a$ (real) and $b$ (imaginary).Explanation:First, compute the square in the denominator:$(2-i)^2 = 4 - 4i + i^2 = 4 - 4i - 1 = 3 - 4i$.Thus, the given number becomes $\frac{1+7i}{3-4i}$.Rationalize by multiplying numerator and denominator by the conjugate $3+4i$:$\frac{1+7i}{3-4i} \cdot \frac{3+4i}{3+4i} = \frac{(1+7i)(3+4i)}{3^2+4^2}$.Expand the numerator: $(1+7i)(3+4i) = 3 + 4i + 21i + 28i^2 = 3 + 25i - 28 = -25 + 25i$.Denominator: $9 + 16 = 25$.Thus, the simplified form is $\frac{-25+25i}{25} = -1 + i$.Here, real part $= -1$ (negative) and imaginary part $= +1$ (positive).A point with negative real and positive imaginary lies in Quadrant 2.Answer:Option D (Quadrant 2).