Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.2

Solution

Given:

z1=13+24i,z2=x+yi,z1z2=27+15iz_1=-13+24i,\quad z_2=x+yi,\quad z_1-z_2=-27+15i (13+24i)(x+yi)=27+15i(13x)+i(24y)=27+15i\begin{aligned} (-13+24i)-(x+yi) &= -27+15i \\ (-13-x)+i(24-y) &= -27+15i \end{aligned}

Compare real and imaginary parts:

13x=27x=1424y=15y=9\begin{aligned} -13-x&=-27 \Rightarrow x=14 \\ 24-y&=15 \Rightarrow y=9 \end{aligned} x=14, y=9\boxed{x=14,\ y=9}