Prove that `((i-sqrt(3))/(i+sqrt(3)))^(100)+((i+sqrt(3))/(i-sqrt(3)))^(100)=-1`

Prove that : (i) sqrt(i)= (1+i)/(sqrt(2)) (ii) sqrt(-i)=(1- i)/(sqrt(2)) (iii) sqrt(i)+sqrt(-i)=sqrt(2)

show that ((sqrt(3)+i)/2)^6+((i-sqrt(3))/2)^6=-2

Simplify :- (i) (6)/(sqrt(2)) (ii) (sqrt(3))/(3) (iii) sqrt((3)/(4)) (iv) (6)/(sqrt(2)) (v) (sqrt(5))/(10) (vi) sqrt((16)/(2))

Find the value of a and b if (i)(sqrt(3)+1)/(sqrt(3)-1)=a+bsqrt(3)" "(ii)(5+2sqrt(3))/(5-2sqrt(3))=a+bsqrt(3)

Rationalise the denominator of each of the following (i) (sqrt(3)+\ 1)/(sqrt(2)) (ii) (sqrt(2)+\ sqrt(5))/(sqrt(3)) (iii) (3sqrt(2))/(sqrt(5))

Express the following expression in the form of a + i b ((3+isqrt(5))(3-isqrt(5)))/((sqrt(3)+sqrt(2)i)-(sqrt(3)-isqrt(2)))

Express the following in the standard form a+i b :((3+isqrt(5))(3-isqrt(5)))/((sqrt(3)+sqrt(2)i)-(sqrt(3)-isqrt(2))) .

Rationalize the denominator of : (i) (2sqrt(3))/sqrt(5)" (ii) "1/(sqrt(3)-sqrt(2))

Simplify : (i) (5+sqrt(5))(5-sqrt(5)) (ii) (3+2sqrt(2))(3-2sqrt(2))

Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(3)-i)/2 d. (-sqrt(3)+i)/2