The locus of z which lies in the shaded regio | vedclass

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Question

(A) The shaded region is centered at $A(-1, 0)$,which corresponds to the complex number $z_0 = -1$. Thus,the distance from $A$ is represented by $|z -

Vedclass · Accepted Answer

$z: |z + 1| > 2, |\arg(z + 1)| < \pi/4$

Vedclass · Answer

(A) The shaded region is centered at $A(-1, 0)$,which corresponds to the complex number $z_0 = -1$. Thus,the distance from $A$ is represented by $|z - (-1)| = |z + 1|$. The region is outside the circle of radius $2$ centered at $A$,so $|z + 1| > 2$. The angular region is bounded by lines passing through $A$ with slopes $\pm 1$,corresponding to angles $\pm \pi/4$. Thus,the argument condition is $|\arg(z + 1)| Combining these,the locus is $z: |z + 1| > 2, |\arg(z + 1)| < \pi/4$.

The locus of $z$ which lies in the shaded region is best represented by

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