Chapter 2: Q56P (page 54)

Describe geometrically the set of points in the complex plane satisfying the following equations.
The angle $z = \frac{π}{2}$ .

Short Answer

Expert verified

The answer is the positive y-axis.

Step by step solution

Given Information

The equation is the angle $z = \frac{π}{2}$ .

Definition of the Complex number

A complex number can be represented 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 the angle of z, $θ = \frac{π}{2}$ .

The complex number is $z = x + y i$ .

And

$\begin{array}{l} z = | z |^{i \frac{π}{2}} \\ z = |z| (c o s \frac{π}{2} + i \sin \frac{π}{2}) \\ z = |z| i \end{array}$

Hence, in the equation, z is purely imaginary, meaning it is the y-axis, and according to the sign, it will be a positive y-axis.

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Describe geometrically the set of points in the complex plane satisfying the following equations.
The angle $z = \frac{π}{2}$ .

Short Answer

Step by step solution

Given Information

Definition of the Complex number

Find the value

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Describe geometrically the set of points in the complex plane satisfying the following equations.The anglez=π2.

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

Turning Points in Physics

Physics of Motion

Dynamics

Energy Physics

Physical Quantities And Units

Fundamentals of Physics

Study anywhere. Anytime. Across all devices.

Describe geometrically the set of points in the complex plane satisfying the following equations.
The angle $z = \frac{π}{2}$ .