`[(sqrt(5)+i/2)(sqrt(5)-i2)]-:(6+i5)`

Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : (i) (5+9i)-:(-3+4i) (ii) [(sqrt(5)+(i)/(2))(sqrt(5)-2i)]-:(6+5i) (iii) ((1-i)(2-i)(3-i))/(1+i) (iv) (1+3i)/((1-2i)^(2))

If x=((sqrt(5)-2))/(sqrt(5)+2) and y=(sqrt(5)+2)/(sqrt(5)-2) find (i)

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) .

(sqrt5 + i sqrt3)(-2 + i)

(5+sqrt(2)i)/(1-2sqrt(i))

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))

(sqrt5 + isqrt3)(-2 + i)

Examine whether the following numbres are rational or irrational: (i) (5-sqrt(5)) (5+sqrt(5)) (ii) (sqrt(3)+2)^(2) (iii) (2sqrt(13))/(3sqrt(52) - 4sqrt(117)) (iv) sqrt(8) + 4sqrt(32) - 6sqrt(2)

Find the following as a single complex number x+iy(sqrt(6)+i5)(sqrt(6)-i(1)/(5))

Simplify by raationalising the denominator. (i) (7sqrt(3) - 5sqrt(2))/(sqrt(48) + sqrt(18)) (ii) (2sqrt(6) -sqrt(5))/(3sqrt(5)-2sqrt(6))