Assess students' understanding of the geometric effects of complex number operations in the complex plane: addition as vector translation, multiplication as rotation and dilation (use polar form), conjugation as reflection across the real axis, and modulus as distance from the origin. Include tasks that require plotting points, converting between rectangular and polar forms, computing images under single and combined operations, and explaining or proving geometric outcomes using arg and |·|. Target grade 9–12 (advanced), medium difficulty, emphasizing interpretation, visualization, and justification.