Formula used:For a complex number z = x + iy|zn| = |z|nWhere, i = ?-1 and|z| = ?(x2 + y2) Calculation:Let, z = \(\left(\frac{?{-3}}{2}-\frac{1}{2}\right)\)? |z200| = \(|\left(\frac{?{-3}}{2}-\frac{1}{2}\right)^{200}|\)Using the property of modulus? |z|200 = \(|\left(\frac{?{-3}}{2}-\frac{1}{2}\right)|^{200}\)We know that |z| = ?(x2 + y2)? |z|200 = \(\left(\sqrt{\frac{(?{-3}}{2})^2+(-\frac{1}{2})^2}\right)^{200}\)? |z|200 = \((\sqrt {\frac{3}{4}+\frac{1}{4}})^{200} = 1^{200}\)? \(\left(\frac{\sqrt{-3}}{2}-\frac{1}{2}\right)^{200}\) = 1