(5-2i)^2

2 min read Jun 16, 2024
(5-2i)^2

Squaring Complex Numbers: (5-2i)^2

In mathematics, 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.

Squaring a complex number like (5-2i) involves multiplying it by itself. Let's break down the steps:

1. Expanding the Expression:

(5-2i)^2 = (5-2i)(5-2i)

2. Applying the FOIL Method:

FOIL stands for First, Outer, Inner, Last. It's a technique to multiply two binomials:

  • First: 5 * 5 = 25
  • Outer: 5 * -2i = -10i
  • Inner: -2i * 5 = -10i
  • Last: -2i * -2i = 4i^2

3. Simplifying using i^2 = -1:

Combining the terms and substituting i^2 with -1:

25 - 10i - 10i + 4(-1) = 25 - 20i - 4

4. Final Result:

Therefore, (5-2i)^2 simplifies to 21 - 20i.

In conclusion, squaring a complex number involves expanding the expression, applying the FOIL method, and simplifying using the property i^2 = -1. The result of (5-2i)^2 is 21 - 20i, another complex number in the form a + bi.

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