MAS111_09_assignment_12 - )) 2 = cos θ + i sin θ . 6....

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NANYANG TECHNOLOGICAL UNIVERSITY MAS 111 FOUNDATION OF MATHEMATICS ASSIGNMENT 12 TUTORIAL DATES: 09, 10, 11/11/2009 1. Multiply (a) (6 - 7 i )(8 + i ), (b) ( 2 3 + 3 2 i )( 2 3 - 3 2 i ), (c) 1 2 + 1 2 i (1 - 2 i ). 2. Express z - 1 in the form z - 1 = a + bi for: (a) z = 6 + 8 i , (b) z = 6 - 8 i , (c) z = (6 + 7 i )(8 - i ). 3. Find (cos θ + i sin θ ) - 1 . 4. Find the polar form for (a) z = 2 2 - 1 2 i , (b) z = 4 i , (c) z = 6 2 + 6 2 i (d) z = - 13 2 + 39 2 3 i . 5. Prove by direct multiplication that (cos( θ 2 ) + i sin( θ 2
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Unformatted text preview: )) 2 = cos θ + i sin θ . 6. Find the 6-th roots of the following complex numbers: (a)-i , (b) 1-i , (c) 3, (d) 16 + 16 √ 2 i . 7. If z is a complex number such that | z | = 1 (i.e. z · ¯ z = 1), compute | 1 + z | 2 + | 1-z | 2 . 8. If x,y are complex numbers, prove that || x | - | y || ≤ | x-y | ....
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MAS111_09_assignment_12 - )) 2 = cos θ + i sin θ . 6....

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