%5E2.jpeg "(7-3i)^2")
Expanding (7-3i)^2
This article will guide you through the steps of expanding the expression (7-3i)^2.
Understanding Complex Numbers
Before we start, let's understand what complex numbers are. 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 i^2 = -1.
Expanding the Expression
To expand (7-3i)^2, we can use the formula (a - b)^2 = a^2 - 2ab + b^2. Here's how it works:
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Identify 'a' and 'b': In this case, a = 7 and b = 3i.
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Substitute the values: (7-3i)^2 = 7^2 - 2(7)(3i) + (3i)^2
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Simplify:
- 7^2 = 49
- 2(7)(3i) = 42i
- (3i)^2 = 9i^2 = 9(-1) = -9
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Combine the terms: 49 - 42i - 9
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Final answer: (7-3i)^2 = 40 - 42i
Conclusion
By using the formula for expanding a binomial squared, we have successfully expanded (7-3i)^2 to get 40 - 42i. This process demonstrates how complex numbers can be manipulated and simplified through algebraic operations.