(−1+4i)⋅(4−3i)

Jasonbradley

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Jun 17, 2024

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Multiplying Complex Numbers: (-1 + 4i) * (4 - 3i)

This article will demonstrate how to multiply two complex numbers: (-1 + 4i) * (4 - 3i).

Understanding Complex Numbers

Complex numbers are numbers of 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).

Multiplication Process

To multiply two complex numbers, we use the distributive property (or FOIL method) just like multiplying binomials in algebra.

1. Distribute: Multiply each term in the first complex number by each term in the second complex number.

   (-1 + 4i) * (4 - 3i) = (-1 * 4) + (-1 * -3i) + (4i * 4) + (4i * -3i)

2. Simplify: Combine real and imaginary terms.

   = -4 + 3i + 16i - 12i²

3. Substitute i² = -1:

   = -4 + 3i + 16i + 12

4. Combine Like Terms:

   = 8 + 19i

Result

Therefore, the product of (-1 + 4i) and (4 - 3i) is 8 + 19i.