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MAS111_09_assignment_12_hints

MAS111_09_assignment_12_hints - MAS 111 FOUNDATION OF...

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MAS 111 FOUNDATION OF MATHEMATICS ASSIGNMENT 12 HINTS 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 ). Hint : Apply the formula ( a + bi )( c + di ) = ( ac - bd ) + ( bc + ad ) 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 ). Hint : I only give z - 1 for z = 6 + 8 i . (6 + 8 i ) - 1 = 1 6 + 8 i = 6 - 8 i (6 + 8 i )(6 - 8 i ) = 6 - 8 i 100 = 3 50 - 2 25 i. Try the others by yourself. 3. Find (cos θ + i sin θ ) - 1 . Hint : 1 cos θ + i sin θ = cos θ - i sin θ (cos θ - i sin θ )(cos θ + i sin θ ) = cos θ - i sin θ. 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 . 1
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Hint : I give solutions to (b) and (d) and leave others to you. (b) 4 i = 4(cos π 2 + i sin π 2 ) (the modulus of 4 i is 4 and the argument is π/ 2). (d)
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MAS111_09_assignment_12_hints - MAS 111 FOUNDATION OF...

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