(2+5i)(3+4i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (2 + 5i)(3 + 4i)

This article will demonstrate the process of multiplying two complex numbers: (2 + 5i) and (3 + 4i).

Understanding Complex Numbers

Complex numbers are numbers that can be 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).

Multiplication Process

To multiply complex numbers, we use the distributive property (also known as FOIL method):

1. First: Multiply the first terms of each complex number: 2 * 3 = 6
2. Outer: Multiply the outer terms: 2 * 4i = 8i
3. Inner: Multiply the inner terms: 5i * 3 = 15i
4. Last: Multiply the last terms: 5i * 4i = 20i²

Now we have: 6 + 8i + 15i + 20i²

Since i² = -1, we can substitute: 6 + 8i + 15i + 20(-1)

Combining the real and imaginary terms: (6 - 20) + (8 + 15)i

Result

Therefore, the product of (2 + 5i) and (3 + 4i) is: -14 + 23i