(7-3i)+(x-2i)^2-(4i+2x^2)

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Expressions: A Step-by-Step Guide

This article will guide you through simplifying the complex expression: (7 - 3i) + (x - 2i)² - (4i + 2x²). We'll break down each step to ensure a clear understanding of the process.

Expanding the Expression

First, we need to expand the squared term:

(x - 2i)² = (x - 2i)(x - 2i)

Using the FOIL method (First, Outer, Inner, Last), we get:

(x - 2i)² = x² - 2xi - 2xi + 4i²

Remember that i² = -1, so we can substitute:

(x - 2i)² = x² - 4xi - 4

Now our expression becomes:

(7 - 3i) + (x² - 4xi - 4) - (4i + 2x²)

Combining Like Terms

Next, we group the real and imaginary terms separately:

(7 - 4) + (x² - 2x²) + (-3i - 4xi - 4i)

Combining the coefficients:

3 + (-x²) + (-7 - 4x)i

Final Result

Therefore, the simplified form of the expression (7 - 3i) + (x - 2i)² - (4i + 2x²) is:

-x² + ( -7 - 4x)i + 3

This expression is now in the standard form of a complex number, a + bi, where a is the real part and b is the imaginary part.