Chapter 2: Q13P (page 74)

Evaluate each of the following in x+ iyform, and compare with a computer solution.
$i^{2 i / π}$

Short Answer

Expert verified

The value of $i^{\frac{2 i}{π}}$ is $e^{[- 1 \bar{+} 2 n π]}$ Where $n = 0, 1, 2, 3, . . . .$ .

Step by step solution

Given Information.

The given number is $i^{\frac{2 i}{π}}$ .

Definition of Complex Numberand Hyperbolic functions.

The numbers that are presented in the form of $x + i y$ where, $' x, y'$ are real numbers and role="math" localid="1658812700788" $' i'$ is an imaginary number, those numbers are referred to as called Complex numbers.

Find the value of i2iπ.

$i^{\frac{2 i}{π}} = e^{[In (i^{\frac{2 i}{π}})]} = e^{[\frac{2 i}{π} (I n (1) + i) (\frac{π}{2} + 2 n π)]} = e^{[\frac{2 i}{π} (i (\frac{π}{2} + 2 n π))]} = e^{[- 1 \bar{+} 2 n π]}$

Where $n = 0, 1, 2, 3, 4, . . . .$

Hence, the solution is in the form of $e^{[- 1 \bar{+} 2 n π]}$ Where $n = 0, 1, 2, 3, . . .$

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Evaluate each of the following in x+ iyform, and compare with a computer solution.
$i^{2 i / π}$

Short Answer

Step by step solution

Given Information.

Definition of Complex Numberand Hyperbolic functions.

Find the value of i2iπ.

One App. One Place for Learning.

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Evaluate each of the following in x+ iyform, and compare with a computer solution.i2i/π

Short Answer

Step by step solution

Given Information.

Definition of Complex Numberand Hyperbolic functions.

Find the value of i2iπ.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Turning Points in Physics

Rotational Dynamics

Particle Model of Matter

Electromagnetism

Astrophysics

Magnetism

Study anywhere. Anytime. Across all devices.

Evaluate each of the following in x+ iyform, and compare with a computer solution.
$i^{2 i / π}$