In Exercises 21–28, divide and express the result in standard ...

Question

In Exercises 21–28, divide and express the result in standard form.

2+3i / 2+i

Accepted Answer

Welcome back everyone to another video, perform the indicated operations on the following complex numbers and have the answer in standard form. We're given a one minus two, I divided by three minus four. I, there are four answer choices. A 11 25th minus 2/5 IB 11 25th plus 2/5 IC 11 25th plus 2 25th I and the 11 25th minus 2 25th I. So essentially, we want to perform a division of two complex numbers, one minus two, I divided by three minus four. I essentially, whenever we have a division, we basically have to multiply both sides of our fraction by the conjugate of the denominator. So we're going to take three minus four I and we're going to change that negative sign into a positive sign. And we have to multiply both sides of the fraction, right, to make sure that it's unchanged. Now, if we look at the bottom, basically we are multiplying two conjugates and the result would be the square of the first term of the square of the real part, which is three squared, right? And then we have to subtract the square of the imaginary part. So four I squared and the square of that is basically four I squared. And in the numerator, we can just rewrite it as one minus two, I multiplied by three plus four I. So we will have to foil it. Let's begin with the numerator. First of all, we multiply one by three which gives us three, then one multiplied by four I, which gives us four, I followed by negative two, I multiplied by three, which is negative six I and finally negative two, I multiplied by four, I gives us negative eight I squared. In the denominator, we can simplify that three squared is nine and four I squared is 16 I squared. Let's recall that I squared is equal to negative one by definition. So now we can rewrite everything as follows. Let's begin with three, then we can combine the like terms or I minus six. I gives us negative to I. And when we subtract negative eight I squared, we're basically adding eight, right? Because I squared is negative one. So we're adding eight and in the denominator we have nine plus 16 because I squared is negative one. So now if we continue, we essentially get three plus eight, this gives us E 11 minus two. I now in the denominator nine plus 16 gives us 25. And now we can separate the real part from the imaginary part. We get 11 divided by 25 minus two, divided by 25 I, which essentially corresponds to the answer choice. D Thank you for watching.

In Exercises 21–28, divide and express the result in standard form.

2+3i / 2+i

Key Concepts

Complex Numbers

Division of Complex Numbers

Standard Form of Complex Numbers

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