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Simplifying Complex Expressions: (-3-3i)^2 - 17i
This article will guide you through simplifying the complex expression (-3-3i)^2 - 17i. We will utilize the properties of complex numbers and algebraic manipulation to arrive at the solution.
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 (i.e., i² = -1).
Simplifying the Expression
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Expanding the square: We start by expanding the square term: (-3-3i)² = (-3-3i) * (-3-3i) = 9 + 9i + 9i + 9i²
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Substituting i²: Since i² = -1, we can substitute it into the expression: 9 + 9i + 9i + 9i² = 9 + 9i + 9i - 9
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Combining like terms: Combining the real and imaginary terms, we get: 9 + 9i + 9i - 9 = 18i
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Adding the remaining term: Now, we add the -17i term: 18i - 17i = i
Final Result
Therefore, the simplified form of the expression (-3-3i)^2 - 17i is i.