Let \( z \) be a complex number of constant modulus such that \( z^{2} \) is purely imaginary th...

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Complex Numbers: Prove that (z-1)/(z+1) is purely imaginary

Let the complex number \(z=x+i y\) be such that \(\frac{2 z-3 i}{2 z+i}\) is purely imaginary. I....

Complex Numbers Formulas -1

Complex Number :If z is complex number such that (𝒛 −𝒊)/(𝒛 −𝟏) is purely imaginary [JEE Main Aug21]

Let z be a purely imaginary number such that lm(z) le 0. Then, arg (z) is equal to | 12 | COMPL...

The Imaginary Unit’s Paradox

complex numbers proving purely real proving purely imaginary

Find all complex numbers z such that (z - 2)[conjugate(z) + i] is a real number.