%5E2.jpeg "(2+7i)^2")
Expanding (2+7i)^2
In mathematics, particularly in the realm of complex numbers, understanding how to expand expressions involving complex numbers is crucial. One such expression is (2+7i)^2. Let's break down the process of expanding this expression.
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 (i.e., i^2 = -1).
Expanding the Expression
To expand (2+7i)^2, we can use the following approach:
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FOIL Method: Apply the FOIL method (First, Outer, Inner, Last) to multiply the binomials: (2 + 7i)(2 + 7i) = 22 + 27i + 7i2 + 7i7i
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Simplify: Combine the terms and remember that i^2 = -1: = 4 + 14i + 14i - 49 = -45 + 28i
Result
Therefore, the expansion of (2+7i)^2 is -45 + 28i. This is a complex number where the real part is -45 and the imaginary part is 28.