" Q."2quad Im(sqrt(a+i sqrt(a^(4)+a^(2)+1)))=

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)

If sum_(i=1)^n(x_i+1)^2=9n and sum_(i=1)^n(x_i-1)^2=5n , then standard deviation of these 'n' observations (x_1) is: (1) 2sqrt(3) (2) sqrt(3) (3) sqrt(5) (4) 3sqrt(2)

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

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)

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

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

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 )

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