Question

Express the given equation in the form of a + ib, a, b ∈ R $i=\sqrt{-1}$. State the values of a and b.
(1 + 2i) (-2 + i)

Answer 1

To express the given equation in the form of a + ib, a, b ∈ R $i=\sqrt{-1}$.

$(1 +2 i)( - 2 + i) \\ \\ = - 2 + i - 4i + 2 {i}^{2} \\ \\ = - 2 - 3i + 2( - 1) \\ \\ = - 2 - 3i - 2 \\ \\ = - 4 - 3i \\ \\ a + ib = - 4 - 3i \\ \\ so \\ \\ a = - 4 \\ \\ b = - 3$
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