document.write( "Question 117518:
\n" ); document.write( "I NEED HELP! :] \n" ); document.write( "

Algebra.Com's Answer #86257 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm assuming P(x) is of the form,
\n" ); document.write( " $\"P%28x%29=ax%5E3%2Bbx%5E2%2Bcx%2Bd\"$
\n" ); document.write( "a) From the properties of i,
\n" ); document.write( " $\"i%5E2=-1\"$
\n" ); document.write( " $\"i%5E3=-i\"$
\n" ); document.write( "So if P(i)=0, then
\n" ); document.write( " $\"P%28i%29=a%28-i%29%2Bb%28-1%29%2Bc%28i%29%2Bd\"$
\n" ); document.write( " $\"P%28i%29=%28d-b%29%2B%28c-a%29i\"$
\n" ); document.write( "For P(i)=0, both the real and complex parts must equal zero.
\n" ); document.write( "Real part
\n" ); document.write( " $\"d-b=0\"$
\n" ); document.write( " $\"highlight%28d=b%29\"$
\n" ); document.write( "Complex part
\n" ); document.write( " $\"c-a=0\"$
\n" ); document.write( " $\"highlight%28c=a%29\"$
\n" ); document.write( "b.) The assumption is d=b and c=a, so let's look at P(-i).
\n" ); document.write( " $\"P%28-i%29=a%28-i%29%5E3%2Bb%2A%28-i%29%5E2%2Bc%28-i%29%2Bd\"$
\n" ); document.write( " $\"%28-i%29%5E3=%28-1%29%5E3%2A%28i%29%5E3=%28-1%29%28-i%29=i\"$
\n" ); document.write( " $\"%28-i%29%5E2=%28-1%29%5E2%2A%28i%29%5E2=%281%29%28-1%29=-1\"$
\n" ); document.write( " $\"P%28-i%29=a%28i%29%2Bb%28-1%29%2Bc%28-i%29%2Bd\"$
\n" ); document.write( " $\"P%28-i%29=%28d-b%29%2B%28a-c%29i\"$
\n" ); document.write( " $\"P%28-i%29=%28b-b%29%2B%28a-a%29i\"$
\n" ); document.write( " $\"P%28-i%29=0\"$
\n" ); document.write( "Yes, then P(-i)=0. \n" ); document.write( "

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