Chapter 2: Q11P (page 74)

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

Short Answer

Expert verified

The x+iy form of the given equation $2^{i} i s, e^{(- 2 n π)} [0.77 + 0.64 i]$

Step by step solution

Given Information.

The given expression is, $2^{i}$ .

Meaning of rectangular form.

Represent the complex number in rectangular form means writing the given complex number in the form of x+iy in which x is the real part and y is the imaginary part.

Convert in rectangular form.

Consider, $w = 2^{i}$ .

Write the given number in polar form.

$w = e^{(i I n (2))}$

Use the logarithm property.

$w = e^{(i I n (2))} w = e^{(i [I n (2) + 2 n π i])} w = e^{(i I n (2) - 2 n π)} w = e^{(i I n (2)) . e x p (- 2 n π)} w = e^{(- 2 n π)} [\cos (I n 2) + i \sin (I n 2)]$

Where $n = 0, \pm 1, \pm 2, \pm 3, . . . .$

$w = [0.77 + 0.64 i] [1 + e^{- 2 π}, e^{(- 4 π)}, . . . .]$

Therefore, x+iy form of the equation $2^{i} i s, e^{(- 2 n π)} [0.77 + 0.64 i] .$

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

Short Answer

Step by step solution

Given Information.

Meaning of rectangular form.

Convert in rectangular form.

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Evaluate each of the following in x+iyform, and compare with a computer solution 2i.

Short Answer

Step by step solution

Given Information.

Meaning of rectangular form.

Convert in rectangular form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Energy Physics

Radiation

Magnetism

Linear Momentum

Force

Thermodynamics

Study anywhere. Anytime. Across all devices.

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