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))

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

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)

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

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

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

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 )

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)