(" ii ")-sqrt(3)-i

Simplify (i) (1 + i)^(18) " " (ii) (-sqrt(3) + 3i)^(31)

Express each of the following in the form (a + ib): (i)" "(i)/((1+i))" "(ii)" "(-1+sqrt(3)i)^(-1)" "(iii)" "(5+sqrt(2)i)/(1=sqrt(2)i)

Rationalize the denominator of : (i) (2sqrt(3))/sqrt(5)" (ii) "1/(sqrt(3)-sqrt(2))

((sqrt(3)+i sqrt(5))(sqrt(3)-i sqrt(5)))/((sqrt(3)+sqrt(2)i)-(sqrt(3)-i sqrt(2))

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

((3+i sqrt(5))(3-i sqrt(5)))/((sqrt(3)+sqrt(2)i)-(sqrt(3)-i sqrt(2)))

Write the lowest rationalising factor of : (i) 5sqrt(2)" (ii) "sqrt(18)-sqrt(50)" (iii) "(2sqrt(2)+2sqrt(3))

Express the following in polar form, (i) sqrt(3)-i (ii) -4+4sqrt(3)i .

Write down the conjugate of each of the following : (i)" "(-5+sqrt(-1))" "(ii)" "(-6-sqrt(-3))" "(iii)" "i^(3)" "(iv)" "(4+5i)^(2)

sqrt(3i)+sqrt(-3i)=(i)+-2sqrt(3)(ii)+-sqrt(6)(iii)3(iv)3i