In Exercises 37–52, perform the indicated operations and write...

Question

In Exercises 37–52, perform the indicated operations and write the result in standard form. ___ ___ √−64 − √−25

Accepted Answer

Welcome back everyone. In this problem, we want to simplify the expression, the square root of negative 121 minus the square root of negative 81. And we want to express our answer in standard form for our answer choices A is two IB is 20. IC is negative two I and D is negative 20 I. Now, if we're going to express it in standard form, what that really means is that we are rewriting it in the standard form for a complex number and recall that for a complex number to write it in standard form means to write it in the form A plus B I where A is the real part and B is the imaginary part. And we'll need to do that because we're finding the square root of a negative number in our problem. And by definition, the unit of an imaginary number I equals the square of negative one. So if, if we can explicitly show the square of negative one in any of our expressions, then we'll get closer to writing it in standard form. So let's go ahead and try to do that. Now, I can rewrite both of my expressions with the, with negative one as a factor. In other words, I can write, rewrite the square root of negative 121 as a square of 121 multiplied by negative one. And I can do the same for 81. So that's 81 multiplied by negative one. Now again, recall that for a radical, OK, the square root of a product A B equals the square of A multiplied by the square of B. So using that idea, I can take it a step further to write it as a square root of 121 multiplied by the square of negative one minus the square of 81 multiplied by the square of negative one. Now, by definition, I have my imaginary units and I can go ahead and simplify. Now the square root of 121 is 11. So I can rewrite that as 11 I and the square root of 81 is nine. So I can write that as nine, I and 11 I minus nine, I equals two. I, no, my number is in standard form because even though I don't have a real part, I have an imaginary part. So my final answer is two. I and when we look in our answer choices that would have been answer choice. A thanks a lot for watching everyone. I hope this video helped.

In Exercises 37–52, perform the indicated operations and write the result in standard form. _ _ √−64 − √−25

Key Concepts

Imaginary Numbers and the Imaginary Unit i

Simplifying Square Roots of Negative Numbers

Standard Form of Complex Numbers

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