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Chapter 2: Q56P (page 54)

Describe geometrically the set of points in the complex plane satisfying the following equations.

The anglez=蟺2.

Short Answer

Expert verified

The answer is the positive y-axis.

Step by step solution

01

Given Information

The equation is the angle z=蟺2.

02

Definition of the Complex number

A complex number can be represented as:


z=x+iy

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

The modulus of a complex number can be calculated as:

|z|=x2+y2

03

Find the value

The equation is the angle of z, 胃=蟺2.

The complex number is z=x+yi.

And

z=|z|i蟺2z=zcos蟺2+isin蟺2z=zi

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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Most popular questions from this chapter

Question:First simplify each of the following numbers to the x+iyform or to therei胃form. Then plot the number in the complex plane.

(1.7-3.2i)2 .

Question: First simplify each of the following numbers to the x+iyform or to the rei胃form. Then plot the number in the complex plane.

5-2i5+2i.

Question:First simplify each of the following numbers to the x+iyform or to there颈胃form. Then plot the number in the complex plane.

(3+i2+i)

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

Use Problems 27 and 28 to find the following absolute values. If you understand Problems 27 and 28 and equation (5.1), you should be able to do these in your head.

|e颈蟺1+i|
See all solutions

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