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

Jasonbradley

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Jun 16, 2024

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

This article will guide you through the process of simplifying the product of two complex numbers, (2 + 3i)(2 - i), and expressing the result in standard form.

Understanding Complex Numbers

A complex number is a number that can be expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, where i² = -1.

The standard form of a complex number is simply writing it in the form a + bi.

Multiplying Complex Numbers

To multiply complex numbers, we use the distributive property, just like we would with binomials.

1. Expand the product: (2 + 3i)(2 - i) = 2(2 - i) + 3i(2 - i)

2. Distribute: = 4 - 2i + 6i - 3i²

3. Substitute i² = -1: = 4 - 2i + 6i + 3

4. Combine real and imaginary terms: = (4 + 3) + (-2 + 6)i

5. Simplify: = 7 + 4i

Conclusion

Therefore, the product of (2 + 3i)(2 - i) expressed in standard form is 7 + 4i.