- #1
Trail_Builder
- 149
- 0
hi
i'm confused at to how my textbook has done the following cancelling :S. hope you can clear things up for me :D
thnx
context: I am looking at complex numbers and De Moivre's Theorem and its consequences Ill use \oslash as the "arguement".
1. [tex]z_{1}z_{2} = r_{1}r_{2}(cos\oslash_{1}cos\oslash_{2} - sin\oslash_{1}sin\oslash_{2} + i(cos\oslash_{1}sin\oslash_{2} + sin\oslash_{1}cos\oslash_{2}))[/tex]
which then cancels to
[tex]z_{1}z_{2} = r_{1}r_{2}(cos(\oslash_{1} + \oslash_{2}) + isin(\oslash_{1} + \oslash_{2}))[/tex]
I see how the [tex]cos(\oslash_{1} + \oslash_{2})[/tex] gets there, but not sure what's going on with the rest :S.
2. [tex]\frac{1}{z} = \frac{1}{r}*\frac{cos\oslash-isin\oslash}{(cos\oslash+isin\oslash)(cos\oslash-isin\oslash)}[/tex]
cancels to
[tex]\frac{1}{z} = \frac{1}{r}*(cos\oslash-isin\oslash)[/tex]
have no idea what's going on there lol.
hope you can help :D
i'm confused at to how my textbook has done the following cancelling :S. hope you can clear things up for me :D
thnx
context: I am looking at complex numbers and De Moivre's Theorem and its consequences Ill use \oslash as the "arguement".
1. [tex]z_{1}z_{2} = r_{1}r_{2}(cos\oslash_{1}cos\oslash_{2} - sin\oslash_{1}sin\oslash_{2} + i(cos\oslash_{1}sin\oslash_{2} + sin\oslash_{1}cos\oslash_{2}))[/tex]
which then cancels to
[tex]z_{1}z_{2} = r_{1}r_{2}(cos(\oslash_{1} + \oslash_{2}) + isin(\oslash_{1} + \oslash_{2}))[/tex]
I see how the [tex]cos(\oslash_{1} + \oslash_{2})[/tex] gets there, but not sure what's going on with the rest :S.
2. [tex]\frac{1}{z} = \frac{1}{r}*\frac{cos\oslash-isin\oslash}{(cos\oslash+isin\oslash)(cos\oslash-isin\oslash)}[/tex]
cancels to
[tex]\frac{1}{z} = \frac{1}{r}*(cos\oslash-isin\oslash)[/tex]
have no idea what's going on there lol.
hope you can help :D