1: Evaluate the equations a) 1 2 ???? 500 ( 0.1 10 6 ) 2500(0.110 6 ) 1 Mathcad entry: 1 / (2 * * 500 * 0.1 * 10^-6) Answer: 3183.10 3183.10 b) ( 1 1 2 120 10 3 0.1 10 6 ) 60 (1 212010 3 0.110 6 1 )60 Mathcad entry: (1 - 1 / (2 * 120 * 10^3 * 0.1 * 10^-6)) * 60 Answer: 249939.00 249939.00 Problem 2: Convert complex numbers into polar form (angle in degrees) 7.7 + 10 ???? 7.7+10j Magnitude: 7.7 2 + 10 2 = 12.66 7.7 2 +10 2 =12.66 Angle: arctan ( 10 7.7 ) = 52.65 arctan( 7.7 10 )=52.65 Answer: 12.66 52.65 12.6652.65 10 26 ???? 1026j Magnitude: 10 2 + ( 26 ) 2 = 27.86 10 2 +(26) 2 =27.86 Angle: arctan ( 26 10 ) = 69.44 arctan( 10 26 )=69.44 Answer: 27.86 69.44 27.8669.44 Problem 3: Convert complex numbers into rectangular form 5 36.87 536.87 ???? = 5 cos ( 36.87 ) = 4.00 , ???? = 5 sin ( 36.87 ) = 3.00 x=5cos(36.87 )=4.00,y=5sin(36.87 )=3.00 Answer: 4 + 3 ???? 4+3j 10 70 1070 ???? = 10 cos ( 70 ) = 3.42 , ???? = 10 sin ( 70 ) = 9.40 x=10cos(70 )=3.42,y=10sin(70 )=9.40 Answer: 3.42 9.40 ???? 3.429.40j Problem 4: Solve Simultaneous Equations System 1: 2 ???? + 3 ???? = 8 , 3 ???? ???? = 23 2x+3y=8,3xy=23 Write in matrix form: [ 2 3 3 1 ] [ ???? ???? ] = [ 8 23 ] [ 2 3 3 1 ][ x y ]=[ 8 23 ] Solution (using Mathcad lsolve or matrix inversion): ???? = 7.57 , ???? = 1.71 x=7.57,y=1.71 Sy