Show that `(1- 2i )/( 3 - 4i ) + (1 + 2i )/( 3 + 4i ) ` is real.

Show that (sqrt(3)/2 + i/2)^3 = i

Simplify [ (1)/(1 - 2i ) + (3)/( 1 + i ) ][ ( 3 + 4i )/( 2 - 4i ) ]

Write (1 +2i ) (1 + 3i ) ( 2 + i ) ^(-1) in the form a + ib

Find real values of theta for which (4 + 3i sin theta) / (1 - 2i sin theta) is purely real.

Show that frac{1-2i}{3-4i} + frac{1+2i}{3+4i} is a real

If a and b are real and ( i ^(4) + 3i ) a + ( i -1) b + 5i ^(3) = 0, find a and b.

Show that (-1+sqrt3 i)^3 is a real number

Simplify: [1 / (1 - 2i) + 3 / (1 + i)] [(3 + 4i) / (2 - 4i)]

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