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Simplify : `{:((i),3(6+6i)+i(6+6i),(ii),(1-i)-(-3+6i)),((iii),((1)/(3)-(2)/(3)i)-(4+(3)/(2)i),(iv),{((1)/(5)+(7)/(5)i)-(6+(1)/(5)i)}-((-4)/(5)+i)):}` |
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Answer» We have `(i)" "3(6+6i)+i(6+6i)=18+18i +6i + 6i^(2)=18 + 24i - 6 = 12 + 24i`. `(ii)" "(1-i)-(-3+6i)=1 - i + 3 - - 6i = 4 - 7i`. `(iii)" "((1)/(3)-(2)/(3)i)-(4+(3)/(3)i)=(1)/(3)-(2)/(3)i - 4 - (3)/(2)i` `" "((1)/(3)-4)-((2)/(3)+(3)/(2))i = (-11)/(3) -(13)/(6)i`. `(iv)" "{((1)/(5)+(7)/(5)i)-(6+(1)/(5)i)}-((-4)/(5)+i)` `" "=((1)/(5)+(7)/(5)i-6-(1)/(5)i)-((-4)/(5)+i)={(1)/(5)-6)+((7)/(5)-(1)/(5))i}-((-4)/(5)+i)` `" "=(-29)/(5)+(6)/(5)i+(4)/(5)-i=((-29)/(5)+(4)/(5))+((6)/(5)i-i)=(-5+(1)/(5)i)`. |
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