Complex Numbers

Question 1

What is Euler’s relation?

Answer 1

Question 2

What is Euler’s identity?

Answer 2

Question 3

How do you easily get large argument in principle argument form

Answer 3

Keep on subtracting multiples of 2pi

Question 4

How do you do the show that equations

Answer 4

Question 5

Answer 5

Remember the 2i in the identity

Question 6

What are the rules for multiplying / dividing complex numbers?

Answer 6

Question 7

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Question 8

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Question 9

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Question 10

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Question 11

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Question 12

What do the following result to (using Euler’s relation)?

Answer 12

Question 13

What do these simplify to?

Answer 13

Question 14

What is the similar exponential identity?

Answer 14

Question 15

Answer 15

A method is more efficient ngl

Question 16

Answer 16

Question 17

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Question 18

Answer 18

Question 19

What is the formula for ?

Answer 19

Question 20

What is the formula for infinite

Answer 20

Question 21

How could you simplify this expression to include sin/cos?

Answer 21

Question 22

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Question 23

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Question 24

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Question 25

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Question 26

Answer 26

Question 27

Solving for when a complex number is real

Answer 27

Question 28

Answer 28

Question 29

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Question 30

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Question 31

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Question 32

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Question 33

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Question 34

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Question 35

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Question 36

Answer 36

To rationalise/ get rid of e. Times by exact same number by negative argument of e

Question 37

Doing x substitutions and solving

Answer 37

Question 38

Using double angle formula

Answer 38

Question 39

The Z method

Answer 39

Question 40

Answer 40

Question 41

Answer 41

Right angled triangle

Question 42

They might want in this type of form

Answer 42

Question 43

Exam Q

Answer 43

Use this format to get exact values

Question 44

Answer 44

Question 45

Answer 45