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1) Amerigo Vespucci has a map of America drawn on the complex plane. The map does not distort distances. Los Angeles corresponds to 0 on this complex plane, and Boston corresponds to 2600i. Meanwhile, Knoxville corresponds to the point 780+1040i. With these city-point correspondences, how far is it from Knoxville to Los Angeles on this complex plane?

2) Determine the complex number z satisfying the equation \( 3z+4i\bar{z}=1-8i\). Note that \(\bar{z}\) denotes the conjugate of z.

 Apr 18, 2019
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1) The distance between Knoxfille and Los Angeles is 780*sqrt(5).

 

2) The solution is z = 7 + i.

 Nov 29, 2019

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