Question

Question given below slove the following equations for r4al x and y .

Answer 1

S={(-24,7/3)}

1) When we're dealing with Complex Numbers we can rewrite this expression:

`(3+4i)^2-2(x-yi)=x+yi`

Considering that their real and their imaginary parts can be taken as equal, so:

`\begin{gathered} (3+4i)^2-2(x-yi)=x+yi \\ (3+4i)^2-2(x-iy) \\ 9+24i+16i^2+2x+2yi \\ \end{gathered}`

2) Rewrite that into the Standard form for complex numbers y= ax +bi combining like terms:

`\begin{gathered} 9+24i-16+2x+2yi \\ (-7-2x)+i(24+2y)\text{ = x+ iy} \\ \end{gathered}`

Finally writing those two expressions as a System of equations we have:

`\begin{gathered} \begin{cases}-7-2x=\text{ x} \\ 24+2y=y\end{cases} \\ -7-2x=x\Rightarrow-7=2x+x\Rightarrow3x=7\Rightarrow(3x)/(3)=(7)/(3) \\ 24+2y=y\Rightarrow24=-2y+y\Rightarrow-y=24\Rightarrow y=-24 \\ S=\mleft\lbrace((7)/(3),-24)\mright\rbrace \end{gathered}`

3) Hence, the answer is S={(-24,7/3)}