Ext2 Complex Numbers: Ellipse as a Locus

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|z - 2| + |z + 2| = 6

This fits under the syllabus dot point(s):
• identify subsets of the complex plane determined by relations, for example |z - 3i| ≤ 4 , π/4 ≤ Arg(z) ≤ 3π/4 , Re(z) ≥ Im(z) and |z - 1| = 2|z - i|

In this video, we look at the ellipse as a locus in the complex plane and try to gain a visualisation of how it is actually formed.
The ellipse is defined as the locus of a point which moves such that the sum of its distances from two fixed points (known as the foci) is a constant.

Note: The study of ellipses is no longer part of the HSC Mathematics Ext 2 course as of the 2020 cohort. Before 2020, it was studied in great detail as part of the old Conics topic. However, this question does appear in some textbooks as a complex numbers locus and is a good question to expand students' understanding.