(7-2i)^2

2 min read Jun 16, 2024
(7-2i)^2

Squaring Complex Numbers: (7-2i)²

This article will walk through the process of squaring the complex number (7-2i).

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.

Squaring (7-2i)

To square (7-2i), we simply multiply it by itself:

(7-2i)² = (7-2i)(7-2i)

We can use the FOIL method (First, Outer, Inner, Last) to expand the product:

  • First: 7 * 7 = 49
  • Outer: 7 * -2i = -14i
  • Inner: -2i * 7 = -14i
  • Last: -2i * -2i = 4i²

Combining the terms, we get:

49 - 14i - 14i + 4i²

Remember that i² = -1. Substituting this into our expression:

49 - 14i - 14i + 4(-1)

Simplifying:

49 - 14i - 14i - 4

Combining real and imaginary terms:

(49 - 4) + (-14 - 14)i

Finally, we arrive at the solution:

(7-2i)² = 45 - 28i

Conclusion

Squaring a complex number involves expanding the expression and simplifying the result, using the knowledge that i² = -1. The result of (7-2i)² is 45 - 28i.

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