-2.jpeg "(−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.