Chapter 2: Q6P (page 76)

Question: Find each of the following in the x + iy form and compare a computer solution.
$\tanh^{- 1} (- i)$

Short Answer

Expert verified

The x + iy form is $z = i (- \frac{π}{4} \pm n π) n = 0, 1, 2, 3, . .$

Step by step solution

Given Information

Given expression is $\tanh^{- 1} (- i)$ .

Definition of Trigonometric equation.

A trigonometric equation is one that has one or more trigonometric ratios with unknown angles.

Use exponential form to expand the equation

Write the exponential form of the $\tanh^{- 1} (- i)$ .

$\frac{e^{(z)} - e^{(z)}}{e^{(z)} + e^{(z)}} = - i$

Multiply numerator and denominator by.

$e^{(2 z)} - 1 = - i e^{(2 z)} - i e^{(2 z)} [i + i] = [1 - i] e^{(2 z)} = \frac{1 - i}{1 + i}$

…(1)

Take both side in equation (1).

$2 z = In (\frac{1 - i}{1 + i}) 2 z = In (\frac{\sqrt{2} e^{(- π i / 4)}}{\sqrt{2} e^{(π i / 4)}}) 2 z = In e^{(- π / 2)} 2 z = In (1) + i (- \frac{π}{2} \pm 2 n π) n = 0, 1, 2, 3, . . 2 z = i (- \frac{π}{2} \pm 2 n π) n = 0, 1, 2, 3, . . 2 z = i (- \frac{π}{4} \pm n π) n = 0, 1, 2, 3, . .$

The x + iy form is $z = i (- \frac{π}{4} \pm n π) n = 0, 1, 2, 3, . .$

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Question: Find each of the following in the x + iy form and compare a computer solution.
$\tanh^{- 1} (- i)$

Short Answer

Step by step solution

Given Information

Definition of Trigonometric equation.

Use exponential form to expand the equation

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Question: Find each of the following in the x + iy form and compare a computer solution.tanh-1(-i)

Short Answer

Step by step solution

Given Information

Definition of Trigonometric equation.

Use exponential form to expand the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Astrophysics

Wave Optics

Fields in Physics

Electricity

Engineering Physics

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

Question: Find each of the following in the x + iy form and compare a computer solution.
$\tanh^{- 1} (- i)$