( – 5+4i)2

2 min read Jun 16, 2024
( – 5+4i)2

Squaring a Complex Number: (-5 + 4i)²

This article will guide you through the process of squaring the complex number (-5 + 4i).

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 (i² = -1).

Squaring the Complex Number

To square (-5 + 4i)², we need to multiply the complex number by itself:

(-5 + 4i)² = (-5 + 4i) * (-5 + 4i)

Now, we can expand this expression using the distributive property (also known as FOIL - First, Outer, Inner, Last):

(-5 + 4i) * (-5 + 4i) = (-5) * (-5) + (-5) * (4i) + (4i) * (-5) + (4i) * (4i)

Simplifying the expression:

= 25 - 20i - 20i + 16i²

Since i² = -1, we can substitute:

= 25 - 20i - 20i - 16

Combining real and imaginary terms:

= (25 - 16) + (-20 - 20)i

= 9 - 40i

Result

Therefore, the square of (-5 + 4i) is 9 - 40i.

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