Polar and Euler Forms

JEE Main Mathematics · Complex Numbers · 4 questions, latest first

• The number of complex numbers z, satisfying |z|=1 and |z/(z̄)+(z̄)/z|=1, is:202523 January, Shift 2 · Q3
• Let z_1, z_2 and z_3 be three complex numbers on the circle |z|=1 with (z_1)=(-π)/4, (z_2)=0 and (z_3)=(π)/4. If |z_1 z̄_2+z_2…202522 January, Shift 1 · Q4
• Let r and θ respectively be the modulus and amplitude of the complex number z=2-i(2 tan (5 π)/8), then (r, θ) is equal to202429 January, Shift 2 · Q2
• The complex number z=(i-1)/(cos (π)/3+i sin (π)/3) is equal to:202331 January, Shift 2 · Q62