Conjugate and Its Properties

JEE Main Mathematics · Complex Numbers · 3 questions, latest first

• Let z be a complex number such that |z|=1. If (2+k^2 z)/(k+z̄)=k z, k ∈ R, then the maximum distance of k+i k^2 from the circle…20252 April, Shift 1 · Q2
• Let z be a complex number such that |z+2|=1 and Im((z+1)/(z+2))=1/5. Then the value of |Rc(z̅+̅2̅)| is20248 April, Shift 1 · Q2
• For a ∈ C, let A={z ∈ C: Re(a+z̄)>Im(ā+z)} and B={z ∈ C: Re(a+z̄)<Im(ā+z)}. Then among the two statements: (S1): If Re(a),…202311 April, Shift 2 · Q3