(sqrt(11))(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 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 + iy, 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) .

(sqrt3+i)^(7)+(sqrt3-i)^(7)

Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : (i) (-5+3i)(8-7i) (ii) (-sqrt(3)+sqrt(-2))(2sqrt(3)-i) (iii) (sqrt(2)-sqrt(3)i)^(2)

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)) iii) (sqrt(3)+sqrt(7))^(2) 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))

Find the values of a and b in each of the following : (a)(5+2sqrt3)/(7+4sqrt(3))=a-6sqrt(3)" "(b)(3-sqrt(5))/(3+2sqrt(5))=asqrt(5)-(19)/(11) (c )(sqrt(2)+sqrt(3))/(3sqrt2-2sqrt(3))=2-bsqrt(6)" "(d)(7+sqrt(5))/(7-sqrt(5))-(7-sqrt(5))/(7+sqrt(5))=a+(7)/(11)sqrt(5b)