document.write( "Question 1122329: Given that the modulus of the complex number |z+1+2i|=3, find the maximum and minimum values of |z-3+i| \n" ); document.write( "

Algebra.Com's Answer #738448 by ikleyn(52811) $\"\"$ $\"About$

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document.write( "The equation  |z+1+2i| = 3  represents the set of points in the complex plane that are remoted in 3 units from the point (-1,-2).\r\n" );
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document.write( "It is the circle of the radius 3 with the center at the point (-1,-2).\r\n" );
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document.write( "So the problem asks to find the minimum and the maximum distance from the point (3,-1) to this circle.\r\n" );
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document.write( "The distance from the center of the circle (-1,-2) to the point (3,-1)  is\r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "This distance is greater than 3, so the point (3,-1) lies outside that circle.\r\n" );
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document.write( "Now, it is very simple to find the maximum distance and the minimum distance from the given point to the circle.\r\n" );
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document.write( "Simply connect the center  (-1,-2) with the point (3,-1) by the straight line.\r\n" );
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document.write( "The minimum will be  -3;  the maximum will be  + 3.\r\n" );
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