Chapter 2: Q34P (page 53)

Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.
${(\frac{1 + i}{1 - i})}^{5}$

Short Answer

Expert verified

The answer is obtained ${|\frac{1 + i}{1 - i}|}^{5} = 1$

Step by step solution

Given information

It is given that $z = {|\frac{1 + i}{1 - i}|}^{5}$

Absolute value of the Complex number

Let z be a complex number consisting of two real numbers as:

$z = x + t y$

Here x and y are the real numbers.

The absolute value of z can be calculated as:

$| z | = \sqrt{x^{2} + y^{2}}$

Begin by stating the given information.

State the given information.

$z = {(\frac{1 + i}{1 - i})}^{5}$

Find the modulus of the function.

$|z| = |{(\frac{1 + i}{1 - i})}^{5}| {|\frac{1 + i}{1 - i}|}^{5}$

The absolute value can be calculated as below:

${|\frac{1 + i}{1 - i}|}^{5} = {(\frac{\sqrt{1 + 1}}{\sqrt{1 + 1}})}^{5} = {(\frac{\sqrt{2}}{\sqrt{2}})}^{5} = 1$

Thus, the final answer is obtained as:

${|\frac{1 + i}{1 - i}|}^{5} = 1$

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Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.
${(\frac{1 + i}{1 - i})}^{5}$

Short Answer

Step by step solution

Given information

Absolute value of the Complex number

Begin by stating the given information.

Find the modulus of the function.

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Most popular questions from this chapter

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Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.(1+i1-i)5

Short Answer

Step by step solution

Given information

Absolute value of the Complex number

Begin by stating the given information.

Find the modulus of the function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Astrophysics

Thermodynamics

Electricity and Magnetism

Dynamics

Mechanics and Materials

Study anywhere. Anytime. Across all devices.

Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.
${(\frac{1 + i}{1 - i})}^{5}$