Perform each operation. Write answers in standard form. (-8+2i...

Question

Perform each operation. Write answers in standard form. (-8+2i)(-1+i)

Accepted Answer

Hello. Everyone in this video we're gonna be looking at this practice problem where we want to perform the multiplication negative 19 plus 17 I times negative three plus five I. And we want to use standard form to write the final answer. So in this case you can see that we're multiplying complex numbers but complex numbers multiply very similar to normal polynomial. Where we can follow the foil method to multiply these two components together. So we follow the foil method. I'll do the first terms first. So negative 19 times negative three which gives me positive 57. Then the outer terms negative 19 times positive five. I is negative 95 I. And the inner terms positive 17 I minus three times negative three is negative 51 i. And finally the last terms of each grouping. So positive 17 I. Times positive five I. Is positive 85 I squared. And in this case recall that I is equal to the square root of negative one. So if I have I squared it's the square root of negative one times the square root of negative one. Or simply negative one. So I'm gonna go back into my expression and replace I squared with negative one. So this becomes 57. I can combine these middle terms To Give Me -146. I Plus 85. And then we have the I squared which I will replace with negative one. So this becomes -146. I -85 will notice I can subtract from 57. And that gives me -28 - i. Well in this case we've combined all the real components and the imaginary components. And this follows the standard form where we have the real part first followed with the imaginary part. So -28 -146. I becomes our final answer for this multiplication, and you can see that it aligns with answer choice. A Hopefully this video, hope and see you next time.

Perform each operation. Write answers in standard form. (-8+2i)(-1+i)

Key Concepts

Complex Number Multiplication

Standard Form of a Complex Number

Properties of the Imaginary Unit i

Watch next