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Chapter 2: Q50P (page 54)

Solve for all possible values of the real numbers x and y in the following equations.|x+iy|=y-ix. .

Short Answer

Expert verified

The possible values are given below:

x=0,y≥0

Step by step solution

01

Given Information 

The equation is|x+iy|=y-ix. .

02

Definition of the Complex number

Every complex number can be represented as:

z=a+bi

Where aand b are both real numbers, z is the complex number, and i is known as iota, which makes z a complex number.

03

Find the values

The equation is x+yi=y-xi..

The value of the modulus must be real and positive so, x=0.

Now the above equation can be written as:

y=iy

Hence, it satisfies all the values of any real positive number.

The possible values are given below:

x=0,y≥0

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Most popular questions from this chapter

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

5-2i5+2i.

Solve for all possible values of the real numbers xand y in the following equations x+iyx-iy=-i.

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

Find the power series for excosxand for exsinxfrom the series for ezin the following way: Write the series for ez; put z=x+iy. Show that ez=ex(cosy+isiny); take real and imaginary parts of the equation, and put y=x.

First simplify each of the following numbers to the x+iyform or to the reiθform. Then plot the number in the complex plane.

(1+i1-i)2.

See all solutions

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