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Write the complex number in rectangular form7( cos T sin w)7( cos T + sln x) = (Simplify your answer; including any radicals Use integers or fractions for any numbe...

Question

Write the complex number in rectangular form7( cos T sin w)7( cos T + sln x) = (Simplify your answer; including any radicals Use integers or fractions for any numbers in the expressic

Write the complex number in rectangular form 7( cos T sin w) 7( cos T + sln x) = (Simplify your answer; including any radicals Use integers or fractions for any numbers in the expressic



Answers

Use a calculator to express each complex number in rectangular form. $$2\left[\cos \left(\frac{4 \pi}{7}\right)+i \sin \left(\frac{4 \pi}{7}\right)\right]$$

Okay, so we've got four times the co sign of seven pi over four, plus I sine of seven pi over four. Okay, so let's see where that is located. That is going to be in the fourth quadrant. It is going to have a pi over four or 45 degree reference angle, which is going to make this route to over two and make this negative or 2/2, substituting those values and for co sign and sign, we could end up getting our final answer here. So initially, we've got four times the co sign, which in this case is route to over to and then because this is negative, it's gonna be in the fourth quarter. It's down route to over two I. And now we have to distribute in combine like terms to get our final answer. Four times were to over two is to root two minus two route to I. And this is the rectangular point. The rectangular coordinate for this whole

We have a complex number given to us in poor form that we want to turn into rectangular form. And to do that, we need to distribute the eight through to the two terms inside our parentheses. And you can just do all that on your calculator if you want and get some decimal answers. But the co sign and the sign of these have exact values because he's involved. 45 45 90 uh, right triangle. So the co sign of seven pi over four is the square root of two over, too. And the sign of seven pi over four is negative square root of two over too times her eye. And then we just need to take those times the eight to put this into rectangular farm. So now, distributing the eight gives us four square root too minus for I square root, too.

We're asked to figure out the rectangular version of this complex number, and so we want to distribute the seven through the parentheses but the co sign and sign of three pi over to have some nice exact answers. So let's figure those out. First co sign of three pi over to is zero, and the sign of three pi over to is negative one. So that becomes minus I times of seven. So zero minus I as negative I time seven gives us negative seven.

Next number on the form Jew Times course I'm the seven degree just nighttime Silas oven degree. Andi were asked to find a credit on this connection number with its country gate. The country arm disconnects number be Jew Times ghosts. I now the anchorman here, will be freed the sign and then becomes a minus seven degree. That's item Sign off. Uh, minus seven decree. So when we want to buy that do complex number, we're going to plan, uh, moderates with the modern us that when we have a Jew square and found our human, we will end him up. So we should get a seven plus seven degree. It isn't becomes a minus because we have Hey, here's a miners and something on the side. 70 cream on a seven decree and we should get Echo Joe Far times. There's one together. Go. Signed is the degree Plus I time signed the decree. This one, we're going to find an answer


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