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# Prove

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Show that the midpoint of the segment connecting $$z_1$$and $$z_2$$ on the complex plane is $$(z_1+z_2)/2$$.

Mar 2, 2022

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I m not sure what I am meant to do to show this.

To me it is just obvious.

Anyway ......if you let

$$z_1=a(cos\theta +isin\theta )\\ z_2=a(cos\alpha +isin\alpha )\\ \text{midpoint will be average of the real parts + average of the imaginary part}\\ midpoint=\frac{a(cos\theta +\cos\alpha)}{2}+\frac{a(sin\theta +\sin\alpha)}{2}\\ midpoint=\frac{a(cos\theta +\cos\alpha)+a(sin\theta +\sin\alpha)}{2}\\ midpoint=\frac{z_1+z_2}{2}\\$$

Mar 3, 2022