If Z = `x^2 - 7x - 9yi` such that `bar Z = y^2 i + 20i - 12` then the number of order pair (x,y) is :

If (x^(4)+2x i)-(3x^(2)+yi)=(3-5i)+(1+2yi) then the number of ordered pairs (x, y) is/are equal to {AA x,y in R and i^(2)=-1}

If x, y, z are integers such that x >=0, y >=1, z >=2 and x + y + z = 15 , then the number of values of ordered triplets (x,y,z) are

If z=x+i y , then show that z bar z +2(z+ bar z )+a=0 , where a in R , represents a circle.

Let A=[(0, 2y,z),(x,y,-z),(x,-y,z)] such that A^(T)A=I , then the value of x^(2)+y^(2)+z^(2) is

z =15x ^(2) +10 xy -6x-4y For which of the ordered pairs, (x,y), below is z ne 0 ?

If x=3i, y=2i, z=m+I, and i=sqrt(-1) , then the expression xy^(2)z=

Let x,y,z in C satisfy |X| = 1,|y-6-8i| = 3 and |z + 1-7i| = 5 respectively, then the minimum value of |x-z| + |y-z| is equal to

Find the ordered pair (x ,y) for which x^2-y^2-i(2x+y)=2idot

Find the values of x and y , if 2 x + 3yi = 2+ 12i , where x, y in R

If z = x + yi, omega = (2-iz)/(2z-i) and |omega|=1 , find the locus of z in the complex plane