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If z=a+ib and |z-2|=|2z-1|prove that a^2...

If z=a+ib and |z-2|=|2z-1|prove that `a^2-b^2=1`

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To solve the problem, we start with the given complex number \( z = a + ib \) and the condition \( |z - 2| = |2z - 1| \). ### Step 1: Express the given condition in terms of \( a \) and \( b \) We can rewrite the expressions inside the absolute values: - \( z - 2 = (a - 2) + ib \) - \( 2z - 1 = 2(a + ib) - 1 = (2a - 1) + 2ib \) ### Step 2: Set up the equation using the modulus ...
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