Theory of Intelligence
11TH•Mathematics•Complex Numbers•Question 2

Solution

If $z_1=-13+24i$ and $z_2=x+yi$, find the real values of $x$ and $y$ such that $z_1-z_2=-27+15i$.

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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+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}

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} x=14, y=9\boxed{x=14,\ y=9}

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