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TASSpecialist MathematicsQuick questions

Unit 3

Quick questions on The Argand diagram and geometry - TCE Mathematics Specialised (Tasmania)

1short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are geometric proof of conjugate facts?
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Because the conjugate reflects in the real axis, the midpoint of the segment from zz to zˉ\bar z always lies on the real axis at Re⁡(z)\operatorname{Re}(z), and the segment itself is vertical. This is the picture behind z+zˉ=2Re⁡(z)z + \bar z = 2\operatorname{Re}(z). Drawing such relationships rather than only manipulating symbols often shortens a proof to one or two lines.

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