Chapter 2: Q29P (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.
${(1 + 2 i)}^{3}$ .

Short Answer

Expert verified

The absolute value is $|z| = 5 \sqrt{5}$ .

Step by step solution

Given Information

The complex number is ${(1 = 2 i)}^{3}$ .

Absolute value of the Complex number

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

$z = x + {}_{z}y$

Here x and y are the real numbers.

The absolute value of z can be calculated as:

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

Find the value

The complex number is ${(1 + 2 i)}^{3}$ .

The absolute value can be calculated as below:

$|z| = {(1 = 2 i)}^{3} = {\sqrt{1 + 4}}^{3} = \sqrt{5} \times \sqrt{5} \times \sqrt{5} |z| = 5 \sqrt{5}$

Thus, the final answer is obtained as:

$|z| = 5 \sqrt{5}$ .

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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.
${(1 + 2 i)}^{3}$ .

Short Answer

Step by step solution

Given Information

Absolute value of the Complex number

Find the value

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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+2i)3.

Short Answer

Step by step solution

Given Information

Absolute value of the Complex number

Find the value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Scientific Method Physics

Oscillations

Waves Physics

Modern Physics

Fundamentals of Physics

Conservation of Energy and Momentum

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.
${(1 + 2 i)}^{3}$ .