document.write( "Question 158029This question is from textbook
\n" ); document.write( ": Hello =)\r
\n" ); document.write( "\n" ); document.write( "I really need help with this problem! If you could help me out that would be great!\r
\n" ); document.write( "\n" ); document.write( "DIRECTIONS: write the complex number is standard form\r
\n" ); document.write( "\n" ); document.write( " $\"+%28sqrt+%282%29+%2F+2+%2B+%28sqrt+%282%29+%2F+2%29+i+%29%5E4+\"$ \r
\n" ); document.write( "\n" ); document.write( "I hope i wrote that right. It's the quantity the squareroot of 2 over 2 plus the squareroot of 2 over 2 times i to the 4th power. I know how to solve it I think but I dont know how to put it in standard form??\r
\n" ); document.write( "\n" ); document.write( "Help me out please! Thank you!!! \n" ); document.write( "

Algebra.Com's Answer #116439 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm assuming that you are in a trig class, and that you have the unit circle with you. Looking at the unit circle, we see that $\"cos%28pi%2F4%29=sqrt%282%29%2F2\"$ and $\"sin%28pi%2F4%29=sqrt%282%29%2F2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"+%28sqrt+%282%29+%2F+2+%2B+%28sqrt+%282%29+%2F+2%29+i+%29%5E4+\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"+%28cos%28pi%2F4%29+%2B+sin%28pi%2F4%29+i+%29%5E4+\"$ Replace $\"sqrt%282%29%2F2\"$ with $\"cos%28pi%2F4%29\"$ and $\"sin%28pi%2F4%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"+cos%284%28pi%2F4%29%29+%2B+sin%284%28pi%2F4%29%29+i+\"$ Use De Moivre's Theorem to expand\r
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\n" ); document.write( "\n" ); document.write( " $\"+cos%28pi%29+%2B+sin%28pi%29+i+\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"-1%2B0%2Ai\"$ Take the cosine of $\"pi\"$ to get -1 and take the sine of $\"pi\"$ to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"-1\"$ Simplify\r
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\n" ); document.write( "\n" ); document.write( "So $\"+%28sqrt+%282%29+%2F+2+%2B+%28sqrt+%282%29+%2F+2%29+i+%29%5E4=-1+\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the answer is in standard form $\"a%2Bbi\"$ where $\"a=-1\"$ and $\"b=0\"$ \n" ); document.write( "

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