208ss216-HW1-solutions - MATH 208 SUMMER II 2016 HW#1 S...

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MATH 208, SUMMER II, 2016 HW #1 S OLUTIONS (1) Show that z = 1 ± i satisfies the equation z 2 - 2 z + 2 = 0 .
(3) Find < i 3 - i 1 2+3 i .
(4) Reduce each of these expressions to a real number: (a) 1+2 i 3 - 4 i + 2 - i 5 i
(b) 5 i (1 - i )(2 - i )(3 - i )
(c) (1 - i ) 4
(5) Use the binomial theorem to find (2 + 3 i ) 4 in the form a + bi . 1
MATH 208, SUMMER II, 2016 2
(6) For any two complex numbers z 1 and z 2 , show that | z 1 + z 2 | 2 + | z 1 - z 2 | 2 = 2 | z 1 | 2 + | z 2 | 2 (7) Show that, when | z | 6 = | z | ,
3 4 < ( z 1 + z 2 ) | z 3 + z 4 | | z 1 | + | z 2 | || z 3 | - | z 4 || .

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