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Quiz9solutions - MAC1105 Quiz#9 Solutions In the top-right...

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Unformatted text preview: MAC1105: Quiz #9 Solutions July 12, 2010 In the top-right corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. 1. For each of the following complex numbers, write in standard form (simply rewrite it if it already is in standard form). If a number is not complex, write not complex: (a) (b) 5i Already in standard form. -(i - 2) = -i + 2 = 2 - i 1+i 3 (c) 0 Already in standard form. (d) = 1 3 + 1i 3 2. Simplify: 1 Write as 57 rst. Now, 57 4 leaves a remainder of 1, so i 1 -1 = i-1 i4 = i3 = -i. i1 = i 318777459186104386922 (b) i As discussed in class, we need only look at the 318777459186104386922 last two digits. 22 4 has a remainder of 2, so i = 2 i = -1. (a) 3. Perform the following operations, and write your answer in standard form: (a) (b) (c) i-57 . 1 i57 = (1 + 2i) - (3 - 4i) = 1 - 3 + 2i - (-4i) = -2 + 6i (5 + i) (2 - 3i) = 10 - 15i + 2i - 3i2 = 10 - 13i + 3 = 13 - 13i 1-i 2 + 3i (1 - i) (2 - 3i) 2 - 3i - 2i + 3i2 -1 - 5i -1 5 = = = - i (2 + 3i) (2 - 3i) 22 - (3i)2 4+9 13 13 1 ...
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