(1-i)-(7-3i)-(2+i)+(6-2i)

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Expressions

This article will guide you through the process of simplifying the complex expression: (1 - i) - (7 - 3i) - (2 + i) + (6 - 2i).

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.

Simplifying the Expression

1. Distribute the negative signs:

   • (1 - i) - (7 - 3i) - (2 + i) + (6 - 2i) = 1 - i - 7 + 3i - 2 - i + 6 - 2i

2. Combine real and imaginary terms:

   • (1 - 7 - 2 + 6) + (-1 + 3 - 1 - 2)i

3. Simplify:

   • -2 - i

Conclusion

The simplified form of the complex expression (1 - i) - (7 - 3i) - (2 + i) + (6 - 2i) is -2 - i.

Remember that when simplifying complex expressions, the key is to treat 'i' as a variable and follow the rules of algebra.