Q&A Given that \cosα+\cosβ+\cosγ=0 and \sinα+\sinβ+\sinγ=0, prove that \sin3α+\sin3β+\sin3γ=3\sin(α+β+γ)
Q&A If z is complex number such that |z|=\dfrac{1}{2}, then find the maximum value of |z^2-z+\dfrac{1}{4}|
Q&A If z_1,z_2\in C such that 2z^2_1+z^2_2=2z_1z_2 and z_1+z_2 is pure imaginary number, show that the complex number expression 3z_1-2z_2 is real number.
Multiple choice If a,x,y are real numbers such that a^2+(4+i)a+2xy+(x-y)i=0, then the trajectory of (x,y) represents a
Multiple choice If z_1, z_2,z_3\in C, then z_1=z_2=z_3 is the for the equation (z_1-z_2)^2+(z_2-z_3)^2=0 to hold true.
Q&A If z \in C, such that the quadratic equation x^2-zx+4+3i=0 has real root.Find z with the least value of the modulus of the complex number.
Q&A If a,b,c are nonzero complex numbers such that \dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{a}, find all possible values for \dfrac{a+b-c}{a-b+c}
Multiple choice If i=\sqrt{-1} , for which of the following values of n does i^n+(-i)^n have a positive values?
