Week 4 2 exercise zup

Week 4 2 exercise zup - Week 4.2 exercise 1 These represent...

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Week 4.2 exercise 1. These represent the same points because adding 180° to an angle and replacing r with –r does not change the point’s location. 2. The point in polar coordinates on the graph would be Point A. 3. x = r cos θ x =− 5cos 5 π 2 =− 5 0 = 0 y = r sin θ y =− 5sin 5 π 2 =− 5 1 =− 5 ( 0, 5 ) 4. r = x 2 + y 2 r = ( 4 ) 2 + ( 4 ) 2 r = 16 + 16 r = 32 r = 5.6568542494923801952067548968388 tan θ = y x = tan 1 4 4 = 3 π 4 ( 4, 4 ) =( 5.657, 3 π 4 ) 5. b 6. | z | = | a + bi | = a 2 + b 2 | z | = 2 2 + 5 2 | z | = 4 + 25 | z | = 29 5.3851648071345040312507104915403
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Week 4.2 exercise
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Unformatted text preview: 7. r =√ a 2 + b 2 r =√ 2 2 +(− 2 ) 2 r =√ 4 + 4 r =√ 8 r =√ 4 ∗ 2 8. 6 ( cos 3 π 2 + i sin 3 π 2 ) 6 ( − i ) − 6 i ( 0, − 6 i ) 9. 5 1 cos sin 4 10 10 i 1 4 − 5 [ cos ( − 5 ∗ π 10 ) + i sin ( − 5 ∗ π 10 ) ] 1 4 − 5 ( − 1 i ) 1024 ( − 1 i ) − 1024 i ( 0, − 1024 i )...
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