Math Problem Statement

(6-i)-(8+2i)

Solution

To simplify the given expression (6i)(8+2i)(6 - i) - (8 + 2i), follow these steps:

  1. Distribute the negative sign across the second set of parentheses: (6i)82i(6 - i) - 8 - 2i

  2. Now, group the real and imaginary parts: (68)+(i2i)(6 - 8) + (-i - 2i)

  3. Simplify the real and imaginary components: 23i-2 - 3i

So, (6i)(8+2i)=23i(6 - i) - (8 + 2i) = -2 - 3i.

Would you like more details on this process or have any further questions?

Here are 5 related questions for further practice:

  1. Simplify (5+3i)(2i)(5 + 3i) - (2 - i).
  2. Add (42i)(4 - 2i) and (1+7i)(1 + 7i).
  3. Subtract (7+6i)(7 + 6i) from (32i)(3 - 2i).
  4. What is the product of (3+i)(3 + i) and (2i)(2 - i)?
  5. Divide (5+i)(5 + i) by (1i)(1 - i).

Tip: When working with complex numbers, always separate the real and imaginary parts for easier calculation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Complex Numbers
Subtraction of Complex Numbers

Formulas

(a + bi) - (c + di) = (a - c) + (b - d)i

Theorems

Properties of Complex Numbers

Suitable Grade Level

Grades 9-12