Find each product and write the result in standard form. (−5 +...

Question

Find each product and write the result in standard form. (−5 + 4i)(3 + i)

Accepted Answer

Welcome back. Everyone. In this problem, we want to multiply negative two plus seven I by 11 plus two I and express our answer in standard form for our answer choices A is negative eight minus 81. IB is negative 36 plus 73. IC is negative eight plus 81. I and D is 36 minus 73. I. Now if we're going to multiply our expressions negative two plus seven I by plus two, I, we can use what we know about the distributive property and we know that we can rewrite this as negative two, multiplied by 11 plus two, I plus seven. I multiplied by 11 plus two. I now negative two multiplied by 11 equals negative 22 and negative two plus two, I equals negative four I seven. I multiplied by 11 is 77 I and seven. I multiplied by two, I equals 14 I squared. Now, before we continue to simplify, there's something that can help us when it comes to I squared. There's a property of complex numbers here because recall that in complex numbers I squared is defined as negative one. And just to jog your memory. That's because I is defined defined as the square root of negative one, which tells us that I squared would be the square root of negative one all squared, which is why it equals negative one. So we can rewrite it here in that form. So by doing that, my problem now becomes negative 22 minus four I plus 77 I plus 14 multiplied by negative one. Now we can combine negative four I and 77 I, because that would have been positive 73 I and 14 multiplied by a negative one is minus 14. We can still combine more like terms because negative 22 and negative are like negative 22 minus 14 equals negative 36. So I can't simplify it any further. I have a real and imaginary part and no, remember we were supposed to write our answer in the standard form for complex numbers. Again, recall that four complex numbers. The standard form would be written as A plus B I. In other words, a real part and an imaginary part. And that's what we have here. The real part is negative 36. The imaginary part is 73 I which tells us then that our answer from the list of answers would be answer. Choice. B Thanks a lot for watching everyone. I hope this video helped.

Find each product and write the result in standard form. (−5 + 4i)(3 + i)

Key Concepts

Complex Number Multiplication

Standard Form of a Complex Number

Imaginary Unit Properties

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