MAS111_09_assignment_12_hints

MAS111_09_assignment_12_hints - MAS 111 FOUNDATION OF...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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)
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/23/2011 for the course MAS 111 taught by Professor Drchansongheng during the Spring '10 term at Nanyang Technological University.

Page1 / 3

MAS111_09_assignment_12_hints - MAS 111 FOUNDATION OF...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online