%5E2.jpeg "(3+7i)^2")
Expanding (3 + 7i)^2
In this article, we'll explore how to expand the expression (3 + 7i)^2, where 'i' represents the imaginary unit (√-1).
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.
Expanding the Expression
To expand (3 + 7i)^2, we can use the FOIL method (First, Outer, Inner, Last) or simply multiply the expression by itself:
(3 + 7i)^2 = (3 + 7i)(3 + 7i)
Expanding using FOIL:
- First: 3 * 3 = 9
- Outer: 3 * 7i = 21i
- Inner: 7i * 3 = 21i
- Last: 7i * 7i = 49i^2
Combining the terms:
9 + 21i + 21i + 49i^2
Remember that i^2 = -1. Substituting this:
9 + 21i + 21i + 49(-1) = 9 + 42i - 49
Simplifying the Result
Finally, combining the real and imaginary terms:
(9 - 49) + 42i = -40 + 42i
Therefore, the expanded form of (3 + 7i)^2 is -40 + 42i.