Find real values of x and y for which the complex numbers ` -5 + ix^(2)y and x^(2) + y + 35 i` are conjugate of each other .

Find real values of x and y for which the complex numbers 7 + ix^(2)y and x^(2) + y + 18i are conjugate of each other.

Find real values of x and y for which the complex numbers -3+ix^(2)y and x^(2)+y+4i are conjugate of each other.

Find real value of xandy for which the complex numbers -3+ix^(2)yandx^(2)+y+4i are conjugate of each other.

The complex numbers sin x - icos 2x and cos x - isin 2x are conjugate to each other for

The complex number sin(x)+i cos(2x) and cos(x)-i sin(2x) are conjugate to each other for

(a) Write the conjugates of the following: (i) 3+i (ii) 3-i (iii) -sqrt(5)-sqrt(7)i (iv) -sqrt(5)i (v) (4)/(5) (vi) 49-(i)/(7) (vii) (1-i)/(1+i) (viii) (1+i)^(2) (ix) (2+5i)^(2) (x) (-2-(1)/(3)i)^(3) (b) Find the real number x and y if: (i) (x-iy)(3+5i) is the conjugate of -6-24 i (ii) -3+ix^(2)y and x^(2)+y+4i are congugate of each other.

Find the real values of x and y for which z_(1)=9y^(2)-4-10ix and z_(2)=8y^(2)-20i are conjugate complex of each other.