(−1−2i) 2

2 min read Jun 17, 2024
(−1−2i) 2

Squaring a Complex Number: (-1 - 2i)²

This article will demonstrate how to square the complex number (-1 - 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.

Squaring a Complex Number

To square a complex number, we simply multiply it by itself:

(-1 - 2i)² = (-1 - 2i) * (-1 - 2i)

Expanding the Product

We can expand this product using the FOIL method (First, Outer, Inner, Last):

  • First: (-1) * (-1) = 1
  • Outer: (-1) * (-2i) = 2i
  • Inner: (-2i) * (-1) = 2i
  • Last: (-2i) * (-2i) = 4i²

Simplifying the Expression

Now we have: 1 + 2i + 2i + 4i²

Remember that i² = -1. Substituting this in:

1 + 2i + 2i + 4(-1) = 1 + 2i + 2i - 4

Combining real and imaginary terms:

(1 - 4) + (2 + 2)i = -3 + 4i

Conclusion

Therefore, (-1 - 2i)² = -3 + 4i. This is another complex number, demonstrating that squaring a complex number can result in another complex number.

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