Multiply polynomial $ \, \color{blue}{ -6+7i } \, $ by $ \, \color{orangered}{ 4+2i }$.

$$ \left( \color{blue}{-6+7i} \right) \cdot \left( \color{orangered}{4+2i} \right) = 14i^2+16i-24 $$

Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= 7i-6 \\ Q(x) &= 2i+4 \\ \end{aligned} $$

In this example we are multiplying two binomials so FOIL method can be used.

$$ \begin{aligned} \left( \color{blue}{ 7i-6}\right) \cdot \left( \color{orangered}{ 2i+4}\right) &= \underbrace{ \color{blue}{7i} \cdot \color{orangered}{2i} }_{\text{FIRST}} + \underbrace{ \color{blue}{7i} \cdot \color{orangered}{4} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-6} \right) \cdot \color{orangered}{2i} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-6} \right) \cdot \color{orangered}{4} }_{\text{LAST}} = \\ &= 14i^2 + 28i + \left( -12i\right) + \left( -24\right) = \\ &= 14i^2 + 28i + \left( -12i\right) + \left( -24\right) = \\ &= 14i^2+16i-24; \end{aligned} $$

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