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

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 are asked to perform addition and subtraction in the given expression and use the standard form to write the final answer. The expression we are given is five radical three minus open parentheses. Two radical three minus seven, I closed parentheses minus five, I plus open parentheses, negative eight radical three plus nine. I closed parentheses. Our answer choices are a five radical three plus 11 I B negative five radical three plus 11 I C negative five radical three minus 11 I D five radical three minus 11. I. The first thing I want to do is I'm going to rewrite my original expression. So I have five radical three minus open parentheses, two radical three minus seven. I closed parentheses minus five I plus open parentheses, negative eight radical three plus nine. I closed parentheses. Before I start combining like terms, I want to eliminate my parentheses. So when I come across the first set of parentheses, I notice it has a negative sign out front. So I'm gonna distribute that negative into the parentheses. So five radical three does not change but I will distribute negative times or sorry, negative multiplied by two radical three. So that'd be negative two radical three and then a negative multiplied by negative seven. I would be a positive seven I, the minus five I does not change, there is a plus sign in front of my next set of parentheses which means that it will not change the value or the signs inside. So I'm going to rewrite this as minus eight radical three plus nine. I now that I've eliminated all of the parentheses, I'm gonna start combining my like terms. In this case, my like terms are gonna be the terms with a radical three and the terms with an I standard form has us, right? The real number part first. So I'm going to combine the radical threes first. So I have five radical three minus two radical three, which would be three radical three and and then minus eight radical three. So this should be negative five radical three. Next, combining the I si have a positive seven I minus five I which would be two I plus nine I. So that's a positive 11 I. So upon combining all my like terms, I get negative five radical three plus 11 I and that's answer choice B have a nice day.

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

Key Concepts

Simplifying Expressions with Radicals

Combining Like Terms

Writing Complex Numbers in Standard Form

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