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Two Sets

Source: 1989 National High School Mathematics League, Exam One, Problem 5

February 25, 2020

Problem Statement

If M={z∈C∣z=t1+t+i1+tt,t∈R,t≠0,t≠−1}M=\{z\in\mathbb{C}|z=\frac{t}{1+t}+\text{i}\frac{1+t}{t},t\in\mathbb{R},t\neq0,t\neq-1\}, N={z∈C∣z=2[cos⁡(arcsin⁡t)+icos⁡(arccos⁡t)],t∈R,∣t∣≤1}N=\{z\in\mathbb{C}|z=\sqrt2[\cos(\arcsin t)+\text{i}\cos(\arccos t)],t\in\mathbb{R},|t|\leq1\}, then ∣M∩N∣|M\cap N| is (A)0(B)1(C)2(D)4\text{(A)}0\qquad\text{(B)}1\qquad\text{(C)}2\qquad\text{(D)}4
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