Chapter 2: Q22P (page 74)

Evaluate each of the following in x+ iyform, and compare with a computer solution.
$\sin (i \ln (\frac{\sqrt{3} + i}{2}))$

Short Answer

Expert verified

The value of $\sin [i \ln (\frac{\sqrt{3} + i}{2})]$ is -0.5 .

Step by step solution

Given Information.

The given number is $\sin [i \ln (\frac{\sqrt{3} + i}{2})] .$

Definition of Complex Number.

The numbers that are presented in the form of $x + iy$ where, $' x, y'$ are real numbers and $' i'$ is an imaginary number, those numbers are referred to as called Complex numbers.

Find the value of sin[i ln(3+i2)].

Let, $u = \sin [i \ln (\frac{\sqrt{3} + i}{2})]$

Use the identity $\sin (i z) = i \sin h (z)$ .

$u = \sin [i \ln (\frac{\sqrt{3} + i}{2})] = i \sin h [\ln (\frac{\sqrt{3} + i}{2})] = i \sin h [I n (r) + i (θ \pm 2 n π)]$

Find the argument and the angle of $\frac{\sqrt{3} + i}{2}$ .

$r = |\frac{\sqrt{3} + i}{2}| = 1 θ = \frac{π}{6}$

$u = i \sinh [\ln (\frac{\sqrt{3} + i}{2})] = i \sinh [\ln (1) + i (\frac{π}{6} \pm 2 nπ)] = i sinhi (\frac{π}{6} \pm 2 nπ) = - \sin (\frac{π}{6} \pm 2 nπ) = - \frac{1}{2} n = 0, 1, 2, 3, . . . .$

Hence, the value of $\sin [i \ln (\frac{\sqrt{3} + i}{2})]$ is -0.5

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Evaluate each of the following in x+ iyform, and compare with a computer solution.
$\sin (i \ln (\frac{\sqrt{3} + i}{2}))$

Short Answer

Step by step solution

Given Information.

Definition of Complex Number.

Find the value of sin[i ln(3+i2)].

One App. One Place for Learning.

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Evaluate each of the following in x+ iyform, and compare with a computer solution.sin(iln(3+i2))

Short Answer

Step by step solution

Given Information.

Definition of Complex Number.

Find the value of sin[i ln(3+i2)].

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

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Atoms and Radioactivity

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Study anywhere. Anytime. Across all devices.

Evaluate each of the following in x+ iyform, and compare with a computer solution.
$\sin (i \ln (\frac{\sqrt{3} + i}{2}))$