Write the complex number $(1 + 2 i)^{3}$ in the form of $a + i b$ .

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Solution

$(1 + 2 i)^{3} = (1)^{3} + 3 (1)^{2} (2 i) + 3 (1) (2 i)^{2} + (2 i)^{3} = 1 + 6 i - 12 - 8 i = - 11 - 2 i$

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