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(12+4i)-(3-7i)

2 min read Jun 16, 2024
(12+4i)-(3-7i)

Subtracting Complex Numbers: A Step-by-Step Guide

This article will guide you through the process of subtracting complex numbers, specifically focusing on the expression (12 + 4i) - (3 - 7i).

Understanding Complex Numbers

Before diving into the subtraction, let's quickly review what complex numbers are:

  • 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.

Subtracting Complex Numbers

To subtract complex numbers, we simply subtract the real and imaginary components separately. Here's how it works:

  1. Distribute the negative sign: Remember that subtracting a complex number is equivalent to adding its negative. Therefore, we can rewrite the expression as:

    (12 + 4i) + (-3 + 7i)

  2. Combine like terms: Group the real terms and the imaginary terms together:

    (12 - 3) + (4 + 7)i

  3. Simplify: Calculate the sum of the real and imaginary components:

    9 + 11i

Conclusion

Therefore, the result of subtracting (3 - 7i) from (12 + 4i) is 9 + 11i.

Key takeaway: Subtracting complex numbers is a straightforward process involving the subtraction of the real and imaginary components separately.

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