document.write( "Question 293596: how do you undo rcis theta?
\n" ); document.write( "if you have a problem such as 4(cos pi/4 + i sin pi/4) how would you put that back into a +bi?
\n" ); document.write( "im not asking for an answer, rather the method to do the problem \n" ); document.write( "

Algebra.Com's Answer #211898 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Hint: For any polar number in the form $\"z=r%28cos%28x%29%2Bi%2Asin%28x%29%29\"$ , where 'r' is the magnitude and 'x' is the angle, it can be converted into rectangular form $\"a%2Bbi\"$ using the following equations:\r
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\n" ); document.write( "\n" ); document.write( "1) $\"r=sqrt%28a%5E2%2Bb%5E2%29\"$ (this can be seen if you draw out a triangle with sides 'a', 'b', and hypotenuse 'r')\r
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\n" ); document.write( "\n" ); document.write( "2) $\"tan%28x%29=b%2Fa\"$ (again this can be seen with a drawing of the triangle) Note: since 'b' is the vertical side, this is the side opposite from the angle 'x'\r
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\n" ); document.write( "\n" ); document.write( "So in this case, $\"r=4\"$ and $\"x=pi%2F4\"$ meaning that $\"4=sqrt%28a%5E2%2Bb%5E2%29\"$ and $\"tan%28pi%2F4%29=b%2Fa\"$ . You'll then find that you'll have two equations and two unknowns which means that you can solve for both 'a' and 'b'.
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