%5E2.jpeg "(2-3i)^2")
Squaring a Complex Number: (2-3i)^2
In this article, we will explore the process of squaring the complex number (2-3i).
Understanding Complex Numbers
Complex numbers are numbers that consist of two parts: a real part and an imaginary part. They are usually written 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 (2-3i)
To square (2-3i), we simply multiply it by itself:
(2-3i)² = (2-3i)(2-3i)
Now, we expand this product using the distributive property (or FOIL method):
= 2(2-3i) - 3i(2-3i) = 4 - 6i - 6i + 9i²
Remember that i² = -1. Substituting this in, we get:
= 4 - 6i - 6i - 9 = -5 - 12i
Conclusion
Therefore, the square of the complex number (2-3i) is -5 - 12i. This process demonstrates how complex numbers can be manipulated and squared using basic algebraic operations.