The complex number 1+7 i (2-i)^2 lies in

Step-by-step solution

Given the complex number z = 1+7i (2-i)^2 . First, expand the denominator: (2-i)^2 = 4 - 4i + i^2 = 4 - 4i - 1 = 3 - 4i . Now, express z as 1+7i 3-4i . Multiply the numerator and denominator by the conjugate of the denominator, which is 3+4i : z = (1+7i)(3+4i) (3-4i)(3+4i) = 3 + 4i + 21i + 28i^2 3^2 + 4^2 = 3 + 25i - 28 9 + 16 = -25 + 25i 25 . Simplifying the expression, we get z = -1 + i . The real part of z is -1 (negative) and the imaginary part is 1 (positive). A complex number with a negative real part and a p