Express each of the following in the form (a + ib) :
`{:((i),(1)/((4+3i)),(ii),((3+4i))/((4-5i)),(iii),((5+sqrt(2)i))/((1-sqrt(2)i))),((iv),((-2+5i))/((3-6i)),(v),((3-4i))/((4-2i)(1+i)),(vi),((2-2i)(2+3i))/((1+2i)(2-i))),((vii),((2+3i))/((2-i)),(viii),((1-i)^(3))/((1-i^(3))),(ix),((1+2i)^(3))/((1+i)(2-i))):}`

Answer

`{:((i),((4)/(25)-(3)/(25)i),(ii),((-8)/(41)+(31)/(41)i),(iii),(1+2 sqrt(2)i),"(iv)",((-4)/(5)+(1)/(15)i)),((v),((1)/(4)-(3)/(4)i),(vi),((63)/(25)-(16)/(25)i),(vii),((-22)/(5)+(19)/(5)i),"(vii)",(-2+0i)),((ix),((-7)/(2)+(1)/(2)i),,,,,,):}`