MathDB

5

Part of 1985 National High School Mathematics League

Problems(1)

Complex Numbers

Source: 1985 National High School Mathematics League, Exam One, Problem 5

2/23/2020
Let Z,W,λZ,W,\lambda be complex numbers, ∣λ∣≠1|\lambda|\neq1. Which statements are correct about the equation Z‾−λZ=W\overline{Z}-\lambda Z=W? I. Z=λ‾W+W‾1−∣λ∣2Z=\frac{\overline{\lambda}W+\overline{W}}{1-|\lambda|^2} is a solution to the equation. II. The equation has only one solution. III. The equation has two solutions. IV. The equation has infinitely many solutions. (A)\text{(A)} Only I and II. (B)\text{(B)} Only I and III. (C)\text{(C)} Only I and IV. (D)\text{(D)} None of (A)(B)(C)\text{(A)(B)(C)}.
complex numbers