Question

Convert the polar representation of this complex number into its standard form: z=6(cos300+isin300)

Answer 1

@zepdrix please help

Answer 2

300 degrees is one of our special angles.
It in quadrant 4.

Answer 3

alright

Answer 4

mhmm

Answer 5

what do i with this?

Answer 6

Do you remember how to find the sine and cosine of your angles in the first quadrant?
30 45 and 60 degrees?

Answer 7

no?

Answer 8

Hmm that makes things kind of difficult.
Haven't you learned about the unit circle and stuff? :o

Answer 9

oh yeah

Answer 10

You could find the reference angle for 300 degrees.
Since we're in quadrant 4, we subtract our angle from 360 degrees.
\(\Large\rm 360^o-\theta=360^o-300^o=60^o\)

Just realize that since we're in quadrant 4, our sine (which represents the y coordinate) should be negative.
\[\Large\rm \sin(300^o)=-\sin(60^o)\]Can you figure out sin(60) using a chart or something maybe? :o
These are values that you should really have memorized.

Answer 11

um....

Answer 12

0.3048106211

Answer 13

It's better if we keep it as an exact value, not a decimal approximation.
http://www.sciencedigest.org/UnitCircle.gif

Answer 14

If you look at the chart, at 300 degrees, the sine is giving us \(\Large\rm -\dfrac{\sqrt3}{2}\)

Answer 15

How about the cosine of 300 degrees?

Answer 16

5pi/3?

Answer 17

No, 5pi/3 is the radian representation of 300 degrees.
Cosine is the first coordinate in the set of brackets.

Answer 18

1/2

Answer 19

Mmmm k good.

Answer 20

\[\Large\rm 6\left(\color{orangered}{\cos300^o}+\mathcal i \color{royalblue}{\sin300^o}\right)\]So plug the values in for sine,\[\Large\rm 6\left(\color{orangered}{\cos300^o}+\mathcal i \color{royalblue}{\frac{-\sqrt3}{2}}\right)\]And cosine,\[\Large\rm 6\left(\color{orangered}{\frac{1}{2}}+\mathcal i \color{royalblue}{\frac{-\sqrt3}{2}}\right)\]And then to finish it up, distribute the 6 to each term and simplify.

Answer 21

so it would be 6/12 and ?

Answer 22

can you please help me simplify?

Answer 23

@zepdrix

Answer 24

@tkhunny can you help me simplify?

Answer 25

You don't know how to simplify it? 0_o

Answer 26

6 times 1/2 = ....?

Answer 27

6/12

Answer 28

@zepdrix i dont know how to simplify the second part

Answer 29

6 times 1/2 = 6/12?
whut....?

Answer 30

Do you remember how to multiply by a fraction?
Because you're not getting the first part right.
\[\Large\rm 6\cdot\frac{1}{2}=\frac{6}{1}\cdot\frac{1}{2}=\frac{6\cdot1}{1\cdot2}=\frac{6}{2}=3\]

Answer 31

For the second part, same idea.\[\Large\rm 6\cdot \mathcal i \frac{(-\sqrt3)}{2}=\frac{6}{1}\cdot \mathcal i \frac{(-\sqrt3)}{2}=\mathcal i\frac{6\cdot(-\sqrt3)}{1\cdot2}=\mathcal i\frac{-6\sqrt3}{2}\]And simplify a little further.
Don't do anything fancy with the i, just leave it there as part of the answer.

Answer 32

I'm really surprised that you're doing this level of math and are unable to multiply fractions :( This is very worrisome.

Answer 33

you really do not need to be rude, i did not mean to put a one, it was a typo, and i was very tired, but thank you for making me feel thoroughly stupid for simply pressing an extra key on my keyboard and not realizing i had done such. I worked my butt off to learn a lot of this math on my own so in all honesty, i think it's perfectly fine that i'm asking questions and what not.

Answer 34

I'm very sorry Jules :(
I'm still learning how to be more patient with people, espcially people who are putting in effort. And you certainly were.

I'm sure you're a very special gal. I didn't mean to make you feel stupid.
Sorry Jules :c Go enjoy a strawberry please.