Chapter 7 Multiple choice questions

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. What are the real and imaginary parts of z = (2 + 3i) / (3 – 2i) ?

Re{z} = 1 and Im{z} = 0. correct incorrect

Re{z} = 0 and Im{z} = 1. correct incorrect

Re{z} = 2/3 and Im{z} = 3/2. correct incorrect

Re{z} = 2/3 and Im{z} = -3/2. correct incorrect

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. What are the modulus and argument of z = –1 – i√3 ?

|z| = 2 and arg{z} = π/3 + 2nπ where n is an integer. correct incorrect

|z| = 2 and arg{z} = 4π/3 + 2nπ where n is an integer. correct incorrect

|z| = 2 and arg{z} = π/6 + 2nπ where n is an integer. correct incorrect

|z| = 2 and arg{z} = 5π/6 + 2nπ where n is an integer. correct incorrect

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. Which of the following is not true about complex numbers?

Re{z₁ + z₂} = Re{z₁} + Re{z₂} correct incorrect

Re{z₁ x z₂} = Re{z₁} x Re{z₂} correct incorrect

|z₁ x z₂| = |z₁| x |z₂| correct incorrect

arg{z₁ x z₂} = arg{ z₁} + arg{ z₂} correct incorrect

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. Which of the following is not true in the context of complex numbers?

An n^th-order polynomial has n roots. correct incorrect

The imaginary part of logarithm is multivalued. correct incorrect

Positive integer powers of a number are unique. correct incorrect

(z + 1)⁷ – (z – 2)⁷ = 0 has 7 roots. correct incorrect

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. Which one of the following hyperbolic relationships is correct?

cosh²(x) – sinh²(x) = 1 correct incorrect

1 + tanh²(x) = sech²(x) correct incorrect

1 + coth²(x) = cosech²(x) correct incorrect

None of the above. correct incorrect