College algebra problem ?

Miss Kelly,

FORGET Dr. NO's answer

2 + i

-------

3 - i

(2 + i) * (3 + i)

-------------------

(3 - i) * (3 + i)

6 + 2i + 3i + i^2

--------------------

.......9 - i^2

6 + 5i - 1

------------

9 - (-1)

5 + 5i

--------

10

1 + i

------

2

1/2 + (1/2)i.....ANSWER

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A PRESENT FOR YOU

Ask someone to write a number, say a five-digit number.

(Can be a 2-digit.....3-digit.....4-digit....ect..…

Suppose the number written is

57836

Now, without showing the asker, you write a number on

a sheet of paper and keep it folded. You have to write the

number by subtracting 2 from the above number and

adding 2 in front which will be....

257834

Next, ask the person to write another five-digit number

below his original number. Suppose he writes 37589.

So you now have...

57836

37589

Now you write a five-digit number below it in such a

way that each digit is 9 minus digit above. You now have...

57836

37589

62410

Ask the person to add one more 5-digit number. If he

adds 54732, you add below it 45267. Note that you decided

the number by subtracting each of his digit from 9.

Thus, you now have.....

57836

37589

62410

54732

45267

Next, ask him to add all the number and he gets 257834

Show him the number which you had written as an answer

to this addition earlier in the folded paper and surprise him.

You have to know a little bit about polar coordinates. I'm pretty sure there isn't a way to simplify this expression while its still in its imaginary and real parts.

1. Convert (2+i) into polar coordinates

The real part and the imaginary parts can be thought of as (x,y) coordinates. In this case the real part is 2 and the imaginary part is 1 which would coorespond to the (2,1). Now to convert to polar coordinates you need to find the magnitude of the line from (0,0) to (2,1) and the angle that this line makes with the positive X axis. The magnitude is Sqrt(2^2 + 1^2) = Sqrt(5) and the angle is just tan(theta) = 1/2, solving for theta we get theta = 26.56 deg

This can be written as Sqrt(5)∟26.56

2. Convert 3-i to polar the same way we get:

Sqrt(10)∟-18.43

3. Dividing the two is a little bit different, since you would just divide the amplitudes as natural and then you have to subtract the bottom angle from the top so we get:

Sqrt(5)∟26.56 / Sqrt(10)∟-18.43 = (√5 / √10) ∟(26.56 + 18.43)

So the answer is just (√(1/2)) ∟45

Now we convert this back to the real and imaginary parts. Since right now we have the magnitude of the line and the angle its at, you just have to noticed its a triangle where we know one angle and the hypoteneus. So the y axis (the imaginary part) is just going to be sin(45) = Im / √(1/2). THe imaginary part is just 1/2. The x axis (the real part) is just going to be cos(45) = Re / √(1/2) so the real part is just 1/2.

Your answer is then just 1/2+1/2i