To prove: The absolute value of a + 0 i according to definition, “The trigonometric form of a complex number x + y i is x + y i = r ( cos θ + i sin θ ) . The number r = x 2 + y 2 is called the absolute value (or modulus) of x + y i ” agrees with the definition | a | = { a i f a ≥ 0 − a i f a < 0 , where a ∈ R and R is ordered field.

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Answer 1

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Chapter 7.3, Problem 28E

To determine

To prove: The absolute value of a+0i according to definition, “The trigonometric form of a complex number x+yi is x+yi=r(cos θ + i sin θ). The number r=x2+y2 is called the absolute value (or modulus) of x+yi” agrees with the definition |a|={ a if a≥0− a if a<0, where a∈R and R is ordered field.

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Answer 2

Question

Chapter 7.3, Problem 28E

To determine

To prove: The absolute value of a+0i according to definition, “The trigonometric form of a complex number x+yi is x+yi=r(cos θ + i sin θ). The number r=x2+y2 is called the absolute value (or modulus) of x+yi” agrees with the definition |a|={ a if a≥0− a if a<0, where a∈R and R is ordered field.

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Answer 3

Question

Chapter 7.3, Problem 28E

To determine

To prove: The absolute value of a+0i according to definition, “The trigonometric form of a complex number x+yi is x+yi=r(cos θ + i sin θ). The number r=x2+y2 is called the absolute value (or modulus) of x+yi” agrees with the definition |a|={ a if a≥0− a if a<0, where a∈R and R is ordered field.

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Answer 4

Question

Chapter 7.3, Problem 28E

To determine

To prove: The absolute value of a+0i according to definition, “The trigonometric form of a complex number x+yi is x+yi=r(cos θ + i sin θ). The number r=x2+y2 is called the absolute value (or modulus) of x+yi” agrees with the definition |a|={ a if a≥0− a if a<0, where a∈R and R is ordered field.

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Answer 5

Chapter 7.3, Problem 28E

To determine

To prove: The absolute value of a+0i according to definition, “The trigonometric form of a complex number x+yi is x+yi=r(cos θ + i sin θ). The number r=x2+y2 is called the absolute value (or modulus) of x+yi” agrees with the definition |a|={ a if a≥0− a if a<0, where a∈R and R is ordered field.

Answer 6

Chapter 7.3, Problem 28E

To determine

To prove: The absolute value of a+0i according to definition, “The trigonometric form of a complex number x+yi is x+yi=r(cos θ + i sin θ). The number r=x2+y2 is called the absolute value (or modulus) of x+yi” agrees with the definition |a|={ a if a≥0− a if a<0, where a∈R and R is ordered field.

Answer 7

Chapter 7.3, Problem 28E

To determine

To prove: The absolute value of a+0i according to definition, “The trigonometric form of a complex number x+yi is x+yi=r(cos θ + i sin θ). The number r=x2+y2 is called the absolute value (or modulus) of x+yi” agrees with the definition |a|={ a if a≥0− a if a<0, where a∈R and R is ordered field.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Solution Summary: The author explains the absolute value of a+0i according to the definition.

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