%5E2.jpeg "(-1+6i)^2")
Squaring a Complex Number: (-1 + 6i)^2
This article will explore the process of squaring the complex number (-1 + 6i).
Understanding Complex Numbers
Complex numbers are 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 + 6i)^2 = (-1 + 6i) * (-1 + 6i)
Expanding the Expression
We can expand this product using the distributive property (or FOIL method):
(-1 + 6i) * (-1 + 6i) = (-1)(-1) + (-1)(6i) + (6i)(-1) + (6i)(6i)
Simplifying the Expression
Simplifying the terms, we get:
1 - 6i - 6i + 36i^2
Since i^2 = -1, we can substitute it into the expression:
1 - 6i - 6i + 36(-1)
Combining the real and imaginary terms:
1 - 36 - 6i - 6i = -35 - 12i
Conclusion
Therefore, the square of the complex number (-1 + 6i) is -35 - 12i.