Given that the complex Z satisfies izi = 1 and iz + 1 / 2I = iz-3 / 2I, find the complex Z

Given that the complex Z satisfies izi = 1 and iz + 1 / 2I = iz-3 / 2I, find the complex Z

Suppose z = a + bi
From | Z | = 1, we can see that a & # 178; + B & # 178; = 1
|z+1/2|² = (a+1/2)²+b²
|z-3/2|² = (a-3/2)²+b²
From | Z + 1 / 2 | = | Z-3 / 2 |, we get
(a+1/2)² + b² = (a-3/2)²+b²
We can get (a + 1 / 2) = (A-3 / 2) or (a + 1 / 2) = - (A-3 / 2). Obviously, the former is not true, and the latter can get a = 1 / 2
B & # 178; = 1-A & # 178; = 1-1 / 4, B = ± (√ 3) / 2
So z = 1 / 2 ± (√ 3) / 2I

Elden Ring Premiere

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