2.jpeg "(−12−3i)2")
Expanding (-12 - 3i)^2
In this article, we'll explore how to expand the complex number (-12 - 3i)^2.
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.
Expanding the Expression
To expand (-12 - 3i)^2, we can use the distributive property (or FOIL method):
(-12 - 3i)^2 = (-12 - 3i) * (-12 - 3i)
Expanding this, we get:
= (-12)(-12) + (-12)(-3i) + (-3i)(-12) + (-3i)(-3i)
= 144 + 36i + 36i + 9i^2
Simplifying with i^2 = -1
We know that i^2 = -1. Substituting this into the expression:
= 144 + 36i + 36i + 9(-1)
= 144 + 72i - 9
Final Result
Simplifying further, we get the final answer:
(-12 - 3i)^2 = 135 + 72i
Therefore, the expansion of (-12 - 3i)^2 is 135 + 72i.