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(-5+6i)-(-2+i)

2 min read Jun 16, 2024
(-5+6i)-(-2+i)

Subtracting Complex Numbers: (-5 + 6i) - (-2 + i)

This article will guide you through the process of subtracting complex numbers, using the example of (-5 + 6i) - (-2 + i).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in 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 (i.e., i² = -1).

Subtracting Complex Numbers

Subtracting complex numbers involves subtracting the real parts and the imaginary parts separately. Here's how to do it:

  1. Distribute the negative sign: (-5 + 6i) - (-2 + i) = -5 + 6i + 2 - i

  2. Combine the real and imaginary terms: (-5 + 2) + (6i - i) = -3 + 5i

Result

Therefore, (-5 + 6i) - (-2 + i) = -3 + 5i.

Key Points

  • Treat real and imaginary parts separately: Remember that you can only add or subtract real numbers with real numbers and imaginary numbers with imaginary numbers.
  • Think of complex numbers as vectors: You can visualize complex numbers as vectors in the complex plane. Subtracting complex numbers is equivalent to finding the difference between two vectors.

By understanding these simple steps, you can confidently subtract any two complex numbers.

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