(3-4i)(2+i)

2 min read Jun 16, 2024
(3-4i)(2+i)

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

This article will demonstrate how to multiply two complex numbers: (3-4i)(2+i).

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, defined as the square root of -1 (i² = -1).

Multiplying Complex Numbers

To multiply complex numbers, we use the distributive property, just like we do with real numbers.

  1. Expand the product: (3 - 4i)(2 + i) = 3(2 + i) - 4i(2 + i)

  2. Distribute: = 6 + 3i - 8i - 4i²

  3. Simplify by substituting i² = -1: = 6 + 3i - 8i + 4

  4. Combine real and imaginary terms: = (6 + 4) + (3 - 8)i

  5. Final result: = 10 - 5i

Conclusion

Therefore, the product of (3-4i) and (2+i) is 10 - 5i.

Remember, multiplying complex numbers involves applying the distributive property, simplifying using i² = -1, and then combining real and imaginary terms.

Related Post


Featured Posts