SOLUTION: Proved that (a)arg(z1z2)=arg(z1)+arg(z2) and, (b)arg(z1/z2) =arg(z1)-arg(z2).
Algebra.Com
Question 1144066: Proved that (a)arg(z1z2)=arg(z1)+arg(z2) and, (b)arg(z1/z2) =arg(z1)-arg(z2).
Answer by ikleyn(52817) (Show Source): You can put this solution on YOUR website!
.
Prove that (a) arg(z1*z2) = arg(z1) + arg(z2) and (b) arg(z1/z2) = arg(z1) - arg(z2).
~~~~~~~~~~~~~~~~
See the lesson
- Multiplication and division of complex numbers in complex plane
in this site and find the proof there.
-----------------
On complex numbers, see introductory lessons
- Complex numbers and arithmetical operations on them
- Complex plane
- Addition and subtraction of complex numbers in complex plane
- Multiplication and division of complex numbers in complex plane
- Solved problems on taking roots of complex numbers
- Solved problems on arithmetic operations on complex numbers
- Solved problem on taking square root of complex number
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Complex numbers".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
RELATED QUESTIONS
z1 and z2 are two complex numbers. if |z1+z2|=|z1|+|z2| then show that... (answered by venugopalramana)
If z1 , z2 are two complex numbers , |z1|=|z2| , and Arg(z1 + z2) = pi/4 ,find... (answered by ikleyn)
Given |z1|=|z2| show that arg(z1+z2) = {{{arg((z1+z2)^2)}}}.
I don't how how to use... (answered by ikleyn)
Please help me with this question, Z1=e^iπ/4 and Z2=e^-iπ/3. Find the arg/z/ of z1*z2... (answered by ikleyn)
Please help me solve this question
If arg (z conjugate) = arg (z2), then
A) z2=kz1 (answered by ikleyn)
I am too much confused when it arrives to finding argument of a complex number. Please... (answered by ikleyn)
Please help me solve this question
If arg (z) < O , then arg(-z)-arg(z)=
A) pie... (answered by Alan3354)
True or False: If S, P, and A are the cube roots of a complex number, then... (answered by ikleyn,math_tutor2020)
(i need help with part B of this question)
The complex number v has a modulus 1 and... (answered by jsmallt9)