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 #738423 by Alex.33(110) $\"\"$ $\"About$

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Grab a pencil and blank paper if you can or do it in your imagination.
\n" ); document.write( "We now have a complex number(z+1+2i), it's magnitude is 3. So we draw a circle with radius 3 and center on (0,0), on the complex plane. This represents the endpoints of all possible complex number(z+1+2i)s.\r
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\n" ); document.write( "\n" ); document.write( "To get the endpoint of (z-3+i), we must add (z+1+2i) with (-4-i), which means we must move its endpoint 4 units in the negative imaginary axis' direction and 1 in the nagative real axis' direction. Try do it with random endpoints in the circle-which one gives the longest magnitude(distance to the origin) and smallest?\r
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\n" ); document.write( "\n" ); document.write( "You'll see the answer is pretty simple. The maximum and minimum magnitude both occur when the endpoints of (z+1+2i) are on the line which (-4-i) is on. Now time for calculations.\r
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\n" ); document.write( "\n" ); document.write( "Maximum $\"sqrt%2817%29%2B3\"$
\n" ); document.write( "Minimum $\"sqrt%2817%29-3\"$ \n" ); document.write( "

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