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))])

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)

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

Write the following as complex numbers: (i) 1+sqrt(-1) (ii) 4-sqrt(-5) (iii) (sqrt(3))/(2)-(sqrt(-2))/(7)

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))