document.write( "Question 1014818: Consider the following sequence of complex numbers:
\n" ); document.write( "(3 − 2i) , (3 − 2i)i, (3 − 2i)i^2, (3 − 2i)i^3, (3 − 2i)i^4
\n" ); document.write( "a) Plot the sequence on the complex number plane.
\n" ); document.write( "b) Describe the geometric effect of multiplying by i.
\n" ); document.write( "c) Describe the geometric meaning of i^2= -1 \n" ); document.write( "

Algebra.Com's Answer #631141 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "a) all these points lie in the complex plane on the circle of the radius 5 with the center at the origin of coordinate system (z=0). \r\n" );
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document.write( "    I will not plot them. Please do it yourself.\r\n" );
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document.write( "b) The geometric effect of multiplication by \"i\" is rotation in the angle  (90 degrees) anti-clockwise.\r\n" );
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document.write( "c) The geometric meaning of  = -1 is in that the multiplication of complex numbers by \"i\" two times is the same \r\n" );
document.write( "    as rotation of the complex plane in angle  (180 degrees) anti-clockwise.\r\n" );
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\n" ); document.write( "\n" ); document.write( "You may want to look into my lessons on complex numbers in this site\r
\n" ); document.write( "\n" ); document.write( "REVIEW of lessons on complex numbers.\r
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