Chapter 2: Q60P (page 54)

Describe geometrically the set of points in the complex plane satisfying the following equations. $| z - 1 + i | = 2$ .

Short Answer

Expert verified

This is the equation of the circle with center $(1, - 1)$ and radius $r = 2$ .

Step by step solution

Given Information

The equation is $|z - 1 + i| = 2$ .

Definition of the Complex number

A complex number can be expressed as:

$z = x + i y$

Where z is the complex number, x and y are real numbers, and i is known as iota, whose value is $\sqrt{- 1}$ .

The modulus of a complex number can be calculated as:

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

Find the value

The equation is $|z - 1 + i| = 2$ .

The complex number is $|x + y i - 1 + i| = 2$ .

$\begin{array}{l} |(x + i) + i (y + 1)| = 2 \\ {(x - 1)}^{2} + {(y + 1)}^{2} = 4 \end{array}$

Hence, this is the equation of the circle with center $(1, - 1)$ and radius $r = 2$ .

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Describe geometrically the set of points in the complex plane satisfying the following equations. $| z - 1 + i | = 2$ .

Short Answer

Step by step solution

Given Information

Definition of the Complex number

Find the value

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Most popular questions from this chapter

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Describe geometrically the set of points in the complex plane satisfying the following equations. |z-1+i|=2.

Short Answer

Step by step solution

Given Information

Definition of the Complex number

Find the value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Engineering Physics

Magnetism

Linear Momentum

Solid State Physics

Mechanics and Materials

Modern Physics

Study anywhere. Anytime. Across all devices.

Describe geometrically the set of points in the complex plane satisfying the following equations. $| z - 1 + i | = 2$ .