Question
If $z=x+i y$, find the equations of the two loci defined by:(a) $|z-4|=3$(b) $\arg (z+2)=\frac{\pi}{6}$
Step 1
We can rewrite $z$ as $x+iy$ and then substitute it into the equation. Show more…
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Key Concepts
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If $z=x+\hbar y$, determine the equations of the two loci: (a) $\left|\frac{z+2}{z}\right|=3$ and (b) $\arg \left\{\frac{z+2}{z}\right\}=\frac{\pi}{4}$
Complex numbers 2
Further problems
If $z=x+j y$, determine the equations of the two loci: (a) $\left|\frac{z+2}{z}\right|=3 \quad$ and (b) $\arg \left\{\frac{z+2}{z}\right\}=\frac{\pi}{4}$
Further problems F.2
If $z=x+j y$, determine the equations of the loci in the Argand diagram, defined by: (a) $\left|\frac{z+2}{z-1}\right|=2$ and (b) arg $\left\{\frac{2-1}{z+2}\right\}=\frac{\pi}{2}$
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