Chapter 2: Q7P (page 76)

Question: Find each of the following in the x + iy form and compare a computer solution.
$\arctan (i \sqrt{2})$

Short Answer

Expert verified

The x + iy form is $z = 0.88 i + (\frac{π}{2} \pm n π)$

Step by step solution

Given Information

Given expression is, $\arctan (i \sqrt{2})$

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

Given the function is, $z = \arctan (i \sqrt{2})$ .

Write the exponential form of the tan(z).

$\tan (z) = - i \frac{e^{(z i)} - e^{(- z i)}}{e^{(z i)} + e^{(- z i)}} - i \frac{e^{(z i)} - e^{(- z i)}}{e^{(z i)} + e^{(- z i)}} = \sqrt{2} i$ …(1)

Simplify equation (1)

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

Take both side in equation (2).

$2 z i = In (\frac{1 - \sqrt{2}}{1 + \sqrt{2}}) = In (0.17) + i (π \pm 2 n π) z = - i \frac{In (0.17)}{2} + (\frac{π}{2} \pm n π) z = 0.88 i + (\frac{π}{2} \pm n π)$

The x + iy form is $z = 0.88 i + (\frac{π}{2} \pm n π)$ .

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Question: Find each of the following in the x + iy form and compare a computer solution.
$\arctan (i \sqrt{2})$

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.arctan(i2)

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

Electrostatics

Fluids

Fundamentals of Physics

Electric Charge Field and Potential

Modern Physics

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Study anywhere. Anytime. Across all devices.

Question: Find each of the following in the x + iy form and compare a computer solution.
$\arctan (i \sqrt{2})$