mat67-Homework1

mat67-Homework1 - MAT067 University of California, Davis...

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MAT067 University of California, Davis Winter 2007 Homework Set 1: Exercises on Complex Numbers Directions : You are assigned the Calculational Problems 1(a, b, c), 2(b), 3(a, b), 4(b, c), 5(a, b), and the Proof-Writing Problems 8 and 11. Please submit your solutions to the Calculational and Proof-Writing Problems separately at the beginning of lecture on Friday January 12, 2007. The two sets will be graded by di±erent persons. 1. Express the following complex numbers in the form x + yi for x, y R : (a) (2 + 3 i ) + (4 + i ) (b) (2 + 3 i ) 2 (4 + i ) (c) 2 + 3 i 4 + i (d) 1 i + 3 1 + i (e) ( i ) - 1 2. Compute the real and imaginary parts of the following expressions, where z is the complex number x + yi and x, y R : (a) 1 z 2 (b) 1 3 z + 2 (c) z + 1 2 z 5 (d) z 3 3. Solve the following equations for z a complex number: (a) z 5 2 = 0 (b) z 4 + i = 0 (c) z 6 + 8 = 0
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2 (d) z 3 4 i = 0 4. Calculate the (a) complex conjugate of the fraction (3 + 8 i ) 4 / (1 + i ) 10
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mat67-Homework1 - MAT067 University of California, Davis...

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