document.write( "Question 1030294: I don't understand what this means? Like I don't understand how to figure out if it's all even or all odd exponents.\r
\n" ); document.write( "\n" ); document.write( "Make a generalization about the exponents of imaginary numbers, regarding whether or not all even or all odd exponents result in real or imaginary numbers. Explain and prove your statement with actual examples and at least one complete sentence that supports your generalization \n" ); document.write( "

Algebra.Com's Answer #645354 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "I don't understand what this means? Like I don't understand how to figure out if it's all even or all odd exponents.\r
\n" ); document.write( "\n" ); document.write( "Make a generalization about the exponents of imaginary numbers, regarding whether or not all even or all odd exponents
\n" ); document.write( "result in real or imaginary numbers. Explain and prove your statement with actual examples and at least
\n" ); document.write( "one complete sentence that supports your generalization
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document.write( "Let us consider the imaginary unit \"i\".\r\n" );
document.write( "Do you know what is it?\r\n" );
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document.write( "It is the complex number such as  = .\r\n" );
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document.write( "Now, consider the sequence of exponents:\r\n" );
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document.write( ", , , ,  . . . and so on.\r\n" );
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document.write( "They ask you: could you tell, which of these numbers are real? imaginary?\r\n" );
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document.write( "It is easy to see that \r\n" );
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document.write( " = -1   (by the definition) is real ;\r\n" );
document.write( " =  =  =  is imaginary;\r\n" );
document.write( " =  =  = 1 is real;\r\n" );
document.write( " =  is imaginary \r\n" );
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document.write( ". . . and so on.\r\n" );
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document.write( "Each odd exponent of an imaginary complex number is an imaginary complex number.\r\n" );
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document.write( "Each even exponent of an imaginary complex number is a real number.\r\n" );
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document.write( "That is all that they want from you.\r\n" );
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