(3-2i)(4+i) In Standard Form

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Numbers: (3 - 2i)(4 + i)

In mathematics, complex numbers are expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, defined as the square root of -1 (i² = -1).

To simplify the expression (3 - 2i)(4 + i), we can use the distributive property (also known as FOIL method) for multiplying binomials:

(3 - 2i)(4 + i) = (3 * 4) + (3 * i) + (-2i * 4) + (-2i * i)

Expanding this:

= 12 + 3i - 8i - 2i²

Now, we can replace i² with -1:

= 12 + 3i - 8i - 2(-1)

Combining the real and imaginary terms:

= 12 + 2 + 3i - 8i

= 14 - 5i

Therefore, the standard form of the product (3 - 2i)(4 + i) is 14 - 5i.