If frac{2+3 i}{i-2}-frac{4 i-3}{3+4 i}=x+i y, | vedclass

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(B) Given the expression $\frac{2+3 i}{i-2}-\frac{4 i-3}{3+4 i}=x+i y$. First,simplify the first term: $\frac{2+3 i}{-2+i} 	imes \frac{-2-i}{-2-i} =

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$-4$

Vedclass · Answer

(B) Given the expression $\frac{2+3 i}{i-2}-\frac{4 i-3}{3+4 i}=x+i y$. First,simplify the first term: $\frac{2+3 i}{-2+i} 	imes \frac{-2-i}{-2-i} = \frac{-4-2i-6i-3i^2}{4+1} = \frac{-4-8i+3}{5} = \frac{-1-8i}{5} = -0.2 - 1.6i$. Next,simplify the second term: $\frac{-3+4i}{3+4i} 	imes \frac{3-4i}{3-4i} = \frac{-9+12i+12i-16i^2}{9+16} = \frac{-9+24i+16}{25} = \frac{7+24i}{25} = 0.28 + 0.96i$. Subtracting the two: $(-0.2 - 1.6i) - (0.28 + 0.96i) = -0.48 - 2.56i$. Thus,$x = -0.48$ and $y = -2.56$. Calculating $3x+y = 3(-0.48) + (-2.56) = -1.44 - 2.56 = -4$.

If $\frac{2+3 i}{i-2}-\frac{4 i-3}{3+4 i}=x+i y$,then $3 x+y=$

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