cheeselover001 cheeselover001

25-09-2014
Mathematics

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(√3/2-1/2i)^2

Express in Stanford form a+bi

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Paweł19 Paweł19

26-09-2014

\(\hbox{From formula:} \\ (a-b)^{2}=a^{2}-2ab+b^{2} \\ \\ (\frac{\sqrt{3}}{2}-\frac{1}{2}i)^{2}=\left( \frac{\sqrt{3}}{2}\right)^{2}-2 \cdot \frac{\sqrt{3}}{2} \cdot \frac{1}{2}i+\left(\frac{1}{2}i\right)^{2}=\frac{3}{4}+\frac{1}{4}i^{2}-\frac{\sqrt{3}}{2}i= \\ = \frac{3}{4}-\frac{1}{4}-\frac{\sqrt{3}}{2}i=\frac{1}{2}-\frac{\sqrt{3}}{2}i \\ \\ \hbox{because} \ \ i^{2}=-1\)

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