document.write( "Question 713186: Find the power of i\r
\n" ); document.write( "\n" ); document.write( "(-i)^42\r
\n" ); document.write( "\n" ); document.write( "A) 1 B)None C) 42i D)i E) -i \n" ); document.write( "

Algebra.Com's Answer #438349 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28-i%29%5E42\"$
\n" ); document.write( "First, we can make things easier if we separate the \"-\" from the \"i\". Using the fact that -i = -1*i and a rule for exponents, $\"%28a%2Ab%29%5En+=+a%5En%2Ab%5En\"$ we can rewrite the expression as:
\n" ); document.write( " $\"%28-1%29%5E42%2Ai%5E42\"$
\n" ); document.write( "Since (-1)*(-1) = 1 and since $\"%28-1%29%5E42\"$ is just 21 pairs of (-1)*(-1), $\"%28-1%29%5E42+=+1\"$ So the expression is now down to:
\n" ); document.write( " $\"i%5E42\"$

\n" ); document.write( "Since $\"i+=+sqrt%28-1%29\"$ , $\"i%5E2+=+-1\"$ . And since $\"i%5E4+=+%28i%5E2%29%5E2\"$ , $\"i%5E4+=+%28-1%29%5E2+=+1\"$ Since $\"i%5E42\"$ is 10 sets of $\"i%5E4\"$ and one $\"i%5E2\"$ , $\"i%5E4+=+-1\"$ :
\n" ); document.write( " $\"i%5E42+=+%28i%5E4%29%5E10%2Ai%5E2+=+1%5E10%2A%28-1%29+=+-1\"$

\n" ); document.write( "So the answer to the problem is B (None). \n" ); document.write( "

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