Simplify (4 – 5i)(3 + 7i) and write the answer in the form a + bi, where a and b are real numbers.
Use foil to multiply the complex numbers:
(4 - 5i)(3 + 7i) = 12 - 15i + 28i -35i^2
Now simplify:
12 + 13i - 35i^2
= 12 + 13i + 35
= 47 + 13i
This is what I got too! Thanks for verifying my work!
To simplify the expression (4 - 5i)(3 + 7i), we can use the distributive property.
First, let's multiply the real parts:
4 * 3 = 12
Next, we'll multiply the imaginary parts:
-5i * 3 = -15i
Now, we'll multiply the real part by the imaginary unit (i):
4 * 7i = 28i
Lastly, we'll multiply the imaginary parts:
-5i * 7i = -35i^2
Since i^2 = -1, we can substitute -1 for i^2:
-35 * -1 = 35
Now, let's combine the terms:
12 + (-15i) + (28i) + 35 = 47 + 13i
So, the simplified form of (4 - 5i)(3 + 7i) is 47 + 13i.
To simplify the expression (4 – 5i)(3 + 7i), we can use the distributive property to multiply the terms together.
First, let's multiply the real numbers:
4 * 3 = 12
Then, we multiply the imaginary parts:
-5i * 7i = -35i^2
Remember that i^2 equals -1, so we can replace i^2 with -1:
-35 * -1 = 35
Multiplying the real and imaginary parts together:
4 * 7i = 28i
Now, we can combine the real and imaginary parts to get the simplified expression:
12 + 35 + 28i
So, the simplified form of (4 – 5i)(3 + 7i) is 47 + 28i.