document.write( "Question 1174590: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.\r
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Algebra.Com's Answer #800258 by AnlytcPhil(1806) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "We draw the graph of the complex number  which is the vector whose tail\r\n" );
document.write( "is at the origin (0,0) and whose tip is at the point (√6,-5). The length of\r\n" );
document.write( "that vector is called r.\r\n" );
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document.write( "Then we draw a perpendicular from (√6,-5) to the x-axis:\r\n" );
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document.write( "we have a right triangle so the angle measured counter-clockwise\r\n" );
document.write( "from the right side of the x-axis, indicated by the red arc. We\r\n" );
document.write( "use the calculator to determine that tan^-1(y/x)=tan^-1(-5/√6)=-63.89986122\r\n" );
document.write( "and we add 360° to get it positive θ=296.1001388°. \r\n" );
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document.write( "We also use the Pythagorean theorem to find r:\r\n" );
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document.write( "The terminal side of any angle is always positive so r=√31.\r\n" );
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document.write( "Next we use DeMovre's theorem to raise everything to the 3rd power, which\r\n" );
document.write( "means we raise the r to the 3rd power and multiply the θ by 3:\r\n" );
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document.write( "Use your TI-84 or TI-83 with MODE DEGREE and MODE a+bi\r\n" );
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document.write( "-169.0147923+34.99999984i\r\n" );
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document.write( "The easy way would be not to bother with DeMoivre's theorem and just type in\r\n" );
document.write( "(√(6)-5i)^3 with MODE set at a+bi, where the key for i is gotten by pressing\r\n" );
document.write( "2nd then the decimal or period key which is the key in the middle at the very\r\n" );
document.write( "bottom row of keys on your calculator.  You'd get -169.0147923+35i, but your\r\n" );
document.write( "teacher specifies that you must use DeMovre's theorem.  So you have to go\r\n" );
document.write( "through all that above. \r\n" );
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document.write( "Edwin

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