" (vii) "(2+3i)/(4+5i)

Prove that: (i) [((3+2i)/(2-5i))+((3-2i)/(2+5i))] is rational (ii) [((2-3i)/(3-4i))((2+3i)/(3+4i))] is real.

Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : (i) (2-3i)/(4-i) (ii) (2+3i)/(-5-4i) (iii) (1+i)/(3+i) (iv) (3+2i)/(4-3i)

Convert each of the following in the form of (a + i b) : (i) 3(1+i)-2(2+3i) (ii) (1)/(4-5i) (iii) (1-2i)^(-2) (iv) (2-3i)/(3+5i) (v) [(1)/(1-2i)+(3)/(1+i)][(3+4i)/(2-4i)]

Simplify and express each of the following in the form (a + ib) : (i)" "((5)/(-3+2i)+(2)/(1-i))((4-5i)/(3+2i))" "(ii)" "((1)/(1-4i)-(2)/(1+i))((1-i)/(5+3i))

(2/(1-i) + 3/(1+i))((2+3i)/(4+5i)) is equal to

(2/(1-i) + 3/(1+i))((2+3i)/(4+5i)) is equal to

Find the square root of the following complex number ((2+3i)/(5-4i) + (2-3i)/(5+4i))

Find the modulus of ((3+2i) (1+i) (2+3i))/((3+4i) (4+5i))

Perform the indicated operations and write the result in the form x+iy: (i) (-3+2i)+(-6+3i) (ii) ((1)/(2)+(7)/(2)i)-(4+(5)/(2)i) (iii) (1-2i)-i+(4-7i)-2i+(5i+3) .