Jasonbradley
Home

(8+5i)(3+2i)-(4+i)(4-i)

less than a minute read Jun 16, 2024
(8+5i)(3+2i)-(4+i)(4-i)

Simplifying Complex Expressions

This article will walk through the steps to simplify the complex expression: (8 + 5i)(3 + 2i) - (4 + i)(4 - i).

Understanding Complex Numbers

Before we begin, let's understand the basics of complex numbers:

  • Complex numbers are numbers of the form a + bi, where:
    • a is the real part
    • b is the imaginary part
    • i is the imaginary unit, defined as the square root of -1 (i² = -1)

Simplifying the Expression

  1. Expand the products:

    • (8 + 5i)(3 + 2i) = 24 + 16i + 15i + 10i²
    • (4 + i)(4 - i) = 16 - i²

  2. Substitute i² with -1:

    • 24 + 16i + 15i + 10(-1) = 14 + 31i
    • 16 - (-1) = 17

  3. Subtract the simplified terms:

    • (14 + 31i) - 17 = -3 + 31i

Final Answer

Therefore, the simplified form of the expression (8 + 5i)(3 + 2i) - (4 + i)(4 - i) is -3 + 31i.

Related Post

Featured Posts