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.

Guest Apr 18, 2019