-2.jpeg "(5 - 2i 2) 2")
Simplifying Complex Numbers: (5 - 2i)²
This article will guide you through the process of simplifying the complex number expression (5 - 2i)².
Understanding Complex Numbers
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 the square root of -1.
Expanding the Expression
To simplify (5 - 2i)², we can use the FOIL method (First, Outer, Inner, Last) or simply expand it like a binomial squared:
(5 - 2i)² = (5 - 2i)(5 - 2i)
Expanding:
(5 - 2i)(5 - 2i) = 5(5) + 5(-2i) - 2i(5) - 2i(-2i)
Simplifying the Terms
Simplify the multiplication:
25 - 10i - 10i + 4i²
Since i² = -1, substitute it:
25 - 10i - 10i + 4(-1)
Combine the real and imaginary terms:
(25 - 4) + (-10 - 10)i
Final Result
The simplified form of (5 - 2i)² is:
(21 - 20i)