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For complex number z, the minimum value of |z| + |z - cosa - i sina|+|z - 2(cosa + i sina )| is..? Solution) |z| + |z-(e^ia)| + |z-2(e^ia)| we see.....oigin , e^ia , 2e^ia , forms a straight line.and for minimum value..... z must coincide with e^iahence the equation becomes:=|e^ia| + 0 + |-e^ia|=1 + 0 + 1=2(ANS)
Evaluate the log function: Calculate 3log 10 2. Solution: Rule 3. log (A n ) = nlog b A 3log 10 2 = log 10 (2 3 ) = log 10 8 = 0.903
Solve the equation for x and check each solution. 2/(x+3) -3/(4-x) = 2x-2/(x 2 -x-12)
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(1 0 3 21 -1 1 -1 1) find A-1
Graph ( x + 1) 2 /9 -( y - 2) 2 /4 =1 Solution It is a hyperbola. There are in fact two standard forms for a hyperbola. Following are the basics for each form. H
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Proof of the Properties of vector arithmetic Proof of a(v → + w → ) = av → + aw → We will begin with the two vectors, v → = (v 1 , v 2 ,..., v n )and w? = w
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