Find the square of the complex number 2 - 2i and write the answer in the form a + bi
where a and b are real numbers
(2 - 2 i)(2 - 2 i)
= 2 (2-2i) -2i(2-2i)
= 4 - 4i - 4 i + 4i^2
= 4 - 8 i - 4
= -8 i
a = 0
b = -1
sorry, b = -8
Thank you so much:)
You are welcome :)
Well, let's square that complex number:
(2 - 2i)² = (2 - 2i) x (2 - 2i)
Now, let's apply the FOIL method to simplify:
(2 - 2i) x (2 - 2i) = 2 x 2 + 2 x (-2i) + (-2i) x 2 + (-2i) x (-2i)
Simplifying further:
4 - 4i - 4i + 4 = 8 - 8i
So, the square of the complex number 2 - 2i is 8 - 8i.
To find the square of a complex number, you need to use the following formula:
(a + bi)² = (a² - b²) + (2ab)i
For the given complex number 2 - 2i, we can plug in the values into the formula:
(a + bi)² = (2² - (-2)²) + (2 * 2 * (-2))i
Simplifying the equation:
(a + bi)² = (4 - 4) + (-8)i
= 0 - 8i
Therefore, the square of the complex number 2 - 2i is 0 - 8i.