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Lösung 3.3:1b

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First, we write the number 21+i23  in polar form.

Image:3_3_1_b.gif Image:3_3_1_b_text.gif

Thus,

21+i23=1cos3+isin3 

and de Moivre's formula gives

21+i2312=112cos123+isin123=1(cos4+isin4)=1(1+i0)=1.