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Answer :

`{:((i),((1)/(4),(sqrt(3))/(4)i),(ii),((2)/(29)-(5)/(29)i),(iii),((5)/(13)-(1)/(13)i),"(iv)",((4)/(5)-(3)/(5)i)):}`Solution :

Use the formula, `z^(-1) = (bar(z))/(|z|^(2))`. <br> (iii) `z = ((2+3i))/((1+i))xx((1-i))/((1-i))=((5+i))/(2)=((5)/(2)+(1)/(2)i)`. <br> `|z|^(2) = ((25)/(4)+(1)/(4))=(26)/(4)=(13)/(2)and bar(z) = ((5)/(2)+(1)/(2)i)`. <br> `therefore" "z^(-1)=(bar(z))/(|z|^(2))=((5-i))/(2)xx(2)/(13)=((5-i))/(13)=((5)/(13)-(1)/(13)i)`. <br> (iv) `z=((1+i)(1+2i))/((1+3i))=((-1+3i))/((1+3i))xx((1-3i))/((1-3i))=((8+6i))/(10)=((4)/(5)+(3)/(5)i)`. <br> `therefore" "bar(z)=((4)/(5)-(3)/(5)i)-((4-3i))/(5)and |z|^(2) = ((16)/(25)+(9)/(25))=(25)/(25)=1`. <br> `therefore" "z^(-1) = (bar(z))/(|z|^(2))=((4)/(5)-(3)/(5)i)`.