Potencia de un complejo en binómica

, por dani

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(1-2i)^4 =\left( \begin{array}{c} 4 \\ 0 \end{array} \right) \cdot 1^4 \cdot (-2i)^0 +\left( \begin{array}{c} 4 \\ 1 \end{array} \right) \cdot 1^3 \cdot (-2i)^1 +\left( \begin{array}{c} 4 \\ 2 \end{array} \right) \cdot 1^2 \cdot (-2i)^2 +
\left( \begin{array}{c} 4 \\ 3 \end{array} \right) \cdot 1^1 \cdot (-2i)^3 +\left( \begin{array}{c} 4 \\ 4 \end{array} \right) \cdot 1^0 \cdot (-2i)^4 =

= 1 \cdot 1 \cdot 1+ 4 \cdot 1 \cdot (-2i) + 6\cdot 1 \cdot 4i^2 + 4 \cdot 1 \cdot (-8i^3) + 1 \cdot 1 \cdot 16i^4 =
1-8i+24i^2-32i^3+16i^4 =
1-8i- 24 +32i+16 = \fbox{-7+24i}

Calcula (1-2i)^4 usando el Binomio de Newton