[" Q."],[" 33"Im(sqrt(a+i sqrt(a^(4)+a^(2)+1)))=]

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

(i)1/sqrt(2)+sqrt(3)+1/sqrt(2)

The standard deviation of the number 31, 32, 33, …, 46, 47 is a) sqrt((17)/(12)) b) sqrt((47^(2)-1)/(12)) c) 2sqrt(6) d) 4sqrt(3)

If the vectors bar A B=3 hat i+4 hat k and bar A C=5 hat i-2 hat j+4 hat k are the sides of a triangle ABC, then the length of the median through A is (1) sqrt(72) (2) sqrt(33) (3) sqrt(45) (4) sqrt(18)

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))

Express the following in the form of a + ib, where a, b in R , i = sqrt-1 . State the value of a and b. (-sqrt(5) + 2sqrt(-4)) + (1 - (sqrt-9)) + (2 + 3i) (2 - 3i)

([(sqrt(2)+i sqrt(3))+(sqrt(2)-i sqrt(3))])/([(sqrt(3)+1sqrt(2))+(sqrt(3)-1sqrt(2))])

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

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