(" vii ")(sqrt(5)-7i)(sqrt(5)-7i)^(2)+(-2+7i)^(2)

Perform the indicated operation and give your anwer in the form x+iy , where x and y are real numbers and i=sqrt(-1) : (i) ((1)/(2)+(1)/(4)i)(-(2)/(3)-(1)/(4)i) (ii) (5+2i)/(-1+sqrt(3)i) . (iii) (sqrt(5)-7i)(sqrt(5)-7i)^(2)+(-2+7i)^(2) .

Perform the indicated operation and give your answer in the form x+yi , where x and y are real numbers and i= sqrt(-1) (sqrt5-7i) (sqrt5-7i)^(2) + (-2+ 7i)^(2)

Perform the following by the indicated operations. Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : Simply: (i) (sqrt(5)+7i)(sqrt(5)-7i)^(3) (ii) (1+i)(2+3i)(3+4i)(4+5i) (iii) (1+i^(2))+i^(4)+i^(6) .

Perform the indicated operation and give your answer in the form x + iy, where x and y are real numbers and i = sqrt (-1) . (sqrt5-7i)(sqrt5-7i)^2+(-2+7i)^2 .

Simplify : (sqrt5+7i)(sqrt5-7i)^3 .

State, whether the following numbers are rational or not : (i) (2+sqrt(2))^(2)" (ii) "(5+sqrt(5))(5-sqrt(5)) (iii) (sqrt(7)/(5sqrt(2)))^(2)

Simplify the following expressions.(i) (5+sqrt(7))(2+sqrt(5)) (ii) (5+sqrt(5))(5-sqrt(5)) (iv) (sqrt(11)-sqrt(7))(sqrt(11)+sqrt(7))

Classify the following numbers as rational or irrational . i) 5-sqrt(3) ii) sqrt(3)+sqrt(2) iii) (sqrt(2)-2)^(2) iv) (2sqrt(7))/(7sqrt(7))

the value of |((3-i sqrt(2))^(2))/(1+i2)| is equal to (i) (11)/(sqrt(5)) (ii) (18)/(sqrt(7)) (iii) (5)/(sqrt(11)) (iv) (13)/(sqrt(3))

(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.