Complex Number and Quadratic Equations
A complex number z is said to be unimodular if . Suppose z1and z2are complex numbers such that 2−z1z2z1−2z2is unimodular and z2is not unimodular. Then the point z1lies on a :
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The locus of z such that z−1z2 is always real is
For every real number c>0, find all complex numbers z, satisfying the equation z∣z∣+cz+i=0.
The real values of x and y, if (3+i)(1+i)x−2i+(3−i)(2+3i)y+i=i, are respectively
If arg(z+a)=6π and arg(z−a)=32π;a∈R, then
If z+2∣z+1∣+i=0 then z equals
For every real value of a > 0, determine the complex numbers which will satisfy the equation ∣z2∣−2iz+2a(1+i)=0.
Find multiplicative inverse of 3+2i
If the equation ax2+bx+c=0,0<a<b<c, has non real complex roots z1 and z2, then