# Thread: Imaginary Numbers and the Binomial Theorem

1. ## Imaginary Numbers and the Binomial Theorem

(2-3i)^6

2. $(2-3i)^{6} = \left(\begin{array}{cc}6\\0\end{array}\right) 2^{6}(\text{-}3i)^{0}$ $+ \left(\begin{array}{cc}6\\1\end{array}\right) 2^{5}(\text{-}3i)^{1}$ $+ \left(\begin{array}{cc}6\\2\end{array}\right) 2^{4}(\text{-}3i)^{2}$ $+ \left(\begin{array}{cc}6\\3\end{array}\right) 2^{3}(\text{-}3i)^{3}$ $+ \left(\begin{array}{cc}6\\4\end{array}\right) 2^{2}(\text{-}3i)^{4}$ $+ \left(\begin{array}{cc}6\\5\end{array}\right) 2^{1}(\text{-}3i)^{5}$ $+ \left(\begin{array}{cc}6\\6\end{array}\right) 2^{0}(\text{-}3i)^{6}$

3. $\sum_{x=0}^{6}\binom{6}{x} (2)^{6-x}(-3i)^x$

### binomial theorem with imaginary numbers

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