%5E2.jpeg "(4-2i)^2")
Simplifying (4 - 2i)^2
In this article, we will explore how to simplify the expression (4 - 2i)^2, where 'i' represents the imaginary unit (√-1).
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. Complex numbers are essential in various areas of mathematics, physics, and engineering.
Simplifying the Expression
To simplify (4 - 2i)^2, we can use the following steps:
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Expand the square: (4 - 2i)^2 = (4 - 2i) * (4 - 2i)
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Apply the distributive property (FOIL): (4 - 2i) * (4 - 2i) = 44 + 4(-2i) - 2i4 - 2i(-2i)
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Simplify: 16 - 8i - 8i + 4i^2
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Substitute i^2 with -1: 16 - 8i - 8i + 4(-1)
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Combine like terms: 12 - 16i
Therefore, the simplified form of (4 - 2i)^2 is 12 - 16i.
Conclusion
Simplifying complex number expressions like (4 - 2i)^2 involves understanding the properties of complex numbers and applying algebraic operations. By following the steps outlined above, we can efficiently simplify such expressions.