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Multiply and simplify the following complex numbers:
\[
(-2+4 i) \cdot(5+i)
\]
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Answer

So, the product of the complex numbers (-2+4i) and (5+i) is -14 + 18i.

Steps

Step 1 ：Let's denote the complex numbers as z1 = (-2+4i) and z2 = (5+i).

Step 2 ：We can multiply these complex numbers similar to how we multiply binomials, using the distributive property or the FOIL method.

Step 3 ：Applying the FOIL method, we multiply the First terms (-2*5), Outer terms (-2*i), Inner terms (4i*5), and Last terms (4i*i).

Step 4 ：Simplifying these, we get -10, -2i, 20i, and 4i^2. Remember that i^2 = -1.

Step 5 ：Combining these terms, we get -10 -2i + 20i - 4 = -14 + 18i.

Step 6 ：So, the product of the complex numbers (-2+4i) and (5+i) is -14 + 18i.