%5E2-in-standard-form.jpeg "(3-6i)^2 In Standard Form")
Squaring Complex Numbers: (3 - 6i)²
This article will explore how to square the complex number (3 - 6i) and express the result in standard form (a + bi).
Understanding Complex Numbers
Complex numbers are numbers that can be expressed in the form a + bi, where:
- a and b are real numbers
- i is the imaginary unit, defined as the square root of -1 (i² = -1)
Squaring the Complex Number
To square (3 - 6i), we simply multiply it by itself:
(3 - 6i)² = (3 - 6i)(3 - 6i)
Now, we use the distributive property (FOIL method) to expand the product:
(3 - 6i)(3 - 6i) = 3(3) + 3(-6i) - 6i(3) - 6i(-6i)
Simplifying the terms:
= 9 - 18i - 18i + 36i²
Remember that i² = -1, so substituting that in:
= 9 - 18i - 18i + 36(-1)
Combining like terms:
= 9 - 36 - 18i - 18i
= -27 - 36i
Standard Form
Therefore, (3 - 6i)² expressed in standard form is -27 - 36i.