" 12.Im "[sqrt(a+i sqrt(a^(4)+a^(2)+1))]=

Show that ((1)/( sqrt2) + (i)/( sqrt2 )) ^( 10) + ((1)/( sqrt2 ) - (i)/( sqrt2 )) ^( 10 ) = 0

The value of {1/((sqrt(6) - sqrt(5))) + 1/((sqrt(5) + sqrt(4))) + 1/((sqrt(4) + sqrt(3))) - 1/((sqrt(3) - sqrt(2))) + 1/((sqrt(2) - 1))} is :

sqrt(-i) = (1-i)/sqrt2

If i=sqrt(-)1, then 4+5(-(1)/(2)+(i sqrt(3))/(2))^(334)+3(-(1)/(2)+(i sqrt(3))/(2))^(365) is equal to (1)1-i sqrt(3)(2)-1+i sqrt(3)(3)i sqrt(3)(4)-i sqrt(3)

The value of (sqrt(2)+sqrt(bar(z)))^(4)+ and (sqrt(2)-sqrt(bar(z)))^(4) are respectively(where z=4+3sqrt(20)i,i=sqrt(-1))

Show that (1 / sqrt(2) + i / sqrt(2))^10 + (1 / sqrt(2) - i / sqrt(2))^10 = 0 .

Evaluate using binomial theorem: (i) (sqrt(2)+1)^(6) +(sqrt(2)-1)^(6) (ii) (sqrt(5)+sqrt(2))^(4)-(sqrt(5)-sqrt(2))^(4)

Evaluate using binomial theorem: (i) (sqrt(2)+1)^(6) +(sqrt(2)-1)^(6) (ii) (sqrt(5)+sqrt(2))^(4)-(sqrt(5)-sqrt(2))^(4)

Evaluate : (i) i^(135) (ii) i^((1)/(47) (iii) (-sqrt(-1))^(4n +3) , n in N (iv) sqrt(-25) + 3sqrt(-4) + 2 sqrt(-9)

Express the follwing in the form of a + ib, a , b in R i=sqrt ( -1). State the value of a and b. ( - sqrt5 + 2 sqrt ( -4) ) + (1 - sqrt ( -9 ))+ (2 + 3i ) (2 - 3i )