If one root of the equation `z^2-a z+a-1=0i s(1+i),w h e r ea` is a complex number then find the root.

The system of equations |z+1-i|=2 and Re(z)>=1 where z is a complex number has

For a complex number Z, if one root of the equation Z^(2)-aZ+a=0 is (1+i) and its other root is alpha , then the value of (a)/(alpha^(4)) is equal to

If one root of the equation x^(2)-ix-(1+i)=0,(i=sqrt(-1)) is 1+i , find the other root.

Consider the equation 10 z^2-3i z-k=0,w h e r ez is a following complex variable and i^2=-1. Which of the following statements ils true? For real complex numbers k , both roots are purely imaginary. For all complex numbers k , neither both roots is real. For all purely imaginary numbers k , both roots are real and irrational. For real negative numbers k , both roots are purely imaginary.

If (1 – i) is a root of the equation , z^3 - 2 (2 - i) z^2 + (4 - 5 i) z - 1 + 3 i = 0 , then find the other two roots.

Which of the following is/are CORRECT . A) If one root of the equation x^(2)-sqrt(5)x-19=0 is (9-sqrt(5))/(2) ,then the other root is (-9+sqrt(5))/(2) B) If one root of the equation x^(2)-sqrt(5)x-19=0 is (9-sqrt(5))/(2) ,then the other root is (9+sqrt(5))/(2) C) If one root of the equation x^(2)-ix-(1+i)=0 , (i=sqrt(-1)) is 1+i find the other root -1 D) If one root of the equation x^(2)-ix-(1+i)=0 , (i=sqrt(-1)) is 1+i find the other root 1-i

If z_(1) and z_(2) are the roots of the equation az^(2)+bz+c=0,a,b,c in complex number and origin z_(1) and z_(2) form an equilateral triangle,then find the value of (b^(2))/(ac) .

Roots of the equation x^2 + bx + 45 = 0 , b in R lie on the curve |z + 1| = 2sqrt(10) , where z is a complex number then