Solution Given: z1=−13+24i,z2=x+yi,z1−z2=−27+15iz_1=-13+24i,\quad z_2=x+yi,\quad z_1-z_2=-27+15iz1=−13+24i,z2=x+yi,z1−z2=−27+15i (−13+24i)−(x+yi)=−27+15i(−13−x)+i(24−y)=−27+15i\begin{aligned} (-13+24i)-(x+yi) &= -27+15i \\ (-13-x)+i(24-y) &= -27+15i \end{aligned}(−13+24i)−(x+yi)(−13−x)+i(24−y)=−27+15i=−27+15i Compare real and imaginary parts: −13−x=−27⇒x=1424−y=15⇒y=9\begin{aligned} -13-x&=-27 \Rightarrow x=14 \\ 24-y&=15 \Rightarrow y=9 \end{aligned}−13−x24−y=−27⇒x=14=15⇒y=9 x=14, y=9\boxed{x=14,\ y=9}x=14, y=9