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Perform the indicated operation and express the result as a simplified complex number.(-5+4i)-(7-i)...

Question

Perform the indicated operation and express the result as a simplified complex number.(-5+4i)-(7-i)

Perform the indicated operation and express the result as a simplified complex number. (-5+4i)-(7-i)



Answers

Perform the indicated operation and express the result as a simplified complex number.
$(-5+3 i)-(6-i)$

So this problem we have six plus four. I about about I since I was imaginary. We need to multiply it by its conjugated in order to change our denominator to a real number. So in order to keep this the same, we have to also multiply the numerator by its conjugated. So the conjugal of eye is just negative. I two the numerator is is a lot simpler times negative eyes this negative I squared which in turn is just one by definition of I. So the rest of our work is with the numerator. We're gonna vote by negative. I buy both terms up here, so we're gonna have negative six I a negative times four eyes negative for I squared. Now to put our riel expression first, we're gonna have We're gonna deal with the I squared. So I squared is negative ones of negative one times negative four is for And then the 65 stays the same. So it's just four minus six I. And since that's all divide about one, our final answer will just be four minus six. I thank you very much

In this problem, you want to divide to complex numbers. There's a negative five plus three. I did. I write to I now the denominator is ah non rial number. So this expression not fully simplified. However, we can fix that by multiplying both the numerator and denominator by I and doing that fix the problem because inner denominator, we'll have to our times. I just going to be negative too, since I squared is negative one now remains is to calculate the numerator. So to do that, we're going to use the distributive property will have negative five times I plus three I squared and then in the denominator we're going to have True I times I or two I squared, but I scored his negative one. Therefore, the denominator is going to be negative too. Then we can simplify this more by remembering that I squared is negative one. So we haven't negative three. When it's five I over negative truth it. Now they pull apart the real and imaginary. Of course, we're going to get 3/2 plus five over two times I. That is our final answer

And this one we have negative four plus four I. And again we're subtracting. It's attracting negative sex plus nine nine. It's got to be careful of these subtraction problems because I have to distribute this negative throughout the expression. So if you wanted to, you could do it where you just changed all the signs. This will be negative, not I, and we add them down to have negative four plus six is just too and positive for minus nine is negative. Five I and there's not really a way to simplify it any further than that said That will be our final answer. Thank you.

Okay, so for this problem doing problem honest to I and we're gonna just distribute Well, it wants us to take the product of these two. But really, if you just treat this imaginary number as a coefficient in front of that expression, we're just distributing that three I to both parts of this expression. So 1239 times neighbor to I and we're gonna be three times five. Let's give us the three times five is 15 I three items negative. Two eyes negative. Six I square. Okay, so our real part in this case is gonna be our i square terms. So I squared because the definition of eyes negative one so negative six times negative one is positive. Six. And then the imaginary part is just 59. Thank you.


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