(x-2i)^2 Is Equivalent To

Jasonbradley

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Jun 17, 2024

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Understanding (x-2i)²

In mathematics, (x-2i)² represents the square of a complex number. To understand its equivalence, we need to recall the basic rules of complex number arithmetic and the concept of squaring.

Expanding the Expression

We can expand the expression using the FOIL method (First, Outer, Inner, Last):

(x-2i)² = (x-2i)(x-2i)

• First: x * x = x²
• Outer: x * -2i = -2ix
• Inner: -2i * x = -2ix
• Last: -2i * -2i = 4i²

Combining these terms, we get:

(x-2i)² = x² - 2ix - 2ix + 4i²

Simplifying the Expression

We know that i² = -1. Substituting this value into the expression, we get:

(x-2i)² = x² - 4ix + 4(-1)

Therefore, the simplified equivalent expression is:

(x-2i)² = x² - 4ix - 4

Key Takeaways

• Squaring a complex number involves expanding the expression and simplifying using the properties of complex numbers.
• The result of squaring a complex number is another complex number.
• Understanding the equivalence of complex number expressions is crucial for solving equations, simplifying complex calculations, and working with complex number theory.