Find each sum or difference. Write answers in standard form. 3√7 ...

Question

Find each sum or difference. Write answers in standard form. 3√7 - (4√7-i) -4i + (-2√7+5i)

Accepted Answer

Hello everyone. We're going to use addition and subtraction to rewrite the expression five times radical three minus two times radical three minus seven. I minus five. I plus negative eight times radical three plus nine I in standard form first thing to recall is that we cannot combine things that aren't the same. Meaning I can only combine Radical threes with radical threes and eyes with eyes. So to start simplifying this the first thing I'm gonna do is distribute the negative sign into the parentheses. So five times the Square 23 stays put multiplying the negative sign in. I now have minus two times the square and then the negative sign times minus seven. I gives me a positive seven I - I is an in parentheses so that stays put in front of our next set of parentheses is a plus sign. That means that these will not change. So we now have a -8 times the square to three plus nine. I so I got rid of my parentheses and now I'm gonna combine my like terms I'm going to start with my radical threes or the square two threes. So I have a five radical three. A -2 times radical three. And the -8 times radical three recall that when you're combining things with radicals through addition and subtraction are radical is pretty much like a variable, it doesn't change only the numbers in front or the coefficients would change. So five plus negative two is a positive three, positive three plus negative eight will give me negative five Times The Square to three. And now I want to combine my imaginary terms So I have seven I. Negative five I And positive nine i. So combining those seven plus negative five is a positive to positive two plus positive nine gives me positive 11 I. So it looks like I have negative five times the square plus 11. I. This would be in standard form because the imaginary part comes second and the real part comes first. So this is my solution and that is answer choice B. Have a nice day.

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Find each sum or difference. Write answers in standard form. 3√7 - (4√7-i) -4i + (-2√7+5i)

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