%5E2.jpeg "(-3+3i)^2")
Squaring a Complex Number: (-3 + 3i)^2
This article explores the squaring of the complex number (-3 + 3i).
Understanding Complex Numbers
A complex number is a number 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 the Complex Number
To square the complex number (-3 + 3i), we use the distributive property of multiplication:
(-3 + 3i)^2 = (-3 + 3i) * (-3 + 3i)
Expanding this product gives:
(-3 + 3i) * (-3 + 3i) = 9 - 9i - 9i + 9i^2
Since i^2 = -1, we can substitute and simplify:
9 - 9i - 9i + 9i^2 = 9 - 9i - 9i - 9 = -18 - 18i
Conclusion
Therefore, the square of the complex number (-3 + 3i) is -18 - 18i.
This simple example demonstrates how to work with complex numbers and their properties, specifically focusing on squaring them.