2.jpeg "( – 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.