Explanation

lobeflepnoumni

Answered 2021-08-21
Author has **25978** answers

asked 2022-01-17

Argument of the summ of two complex numbers

Let r, s be positive real numbers and \(\displaystyle\theta,\ \phi\) real numbers with \(\displaystyle{\left|\theta-\phi\right|}{ < }\pi\). Then an argument of \(\displaystyle{r}{e}^{{{i}\theta}}+{s}{e}^{{{i}\phi}}\) lies between \(\displaystyle\theta\) and \(\displaystyle\phi\)

Can someone give a short, clean proof of the statement above that doesn't rely on geometric intuition?

Let r, s be positive real numbers and \(\displaystyle\theta,\ \phi\) real numbers with \(\displaystyle{\left|\theta-\phi\right|}{ < }\pi\). Then an argument of \(\displaystyle{r}{e}^{{{i}\theta}}+{s}{e}^{{{i}\phi}}\) lies between \(\displaystyle\theta\) and \(\displaystyle\phi\)

Can someone give a short, clean proof of the statement above that doesn't rely on geometric intuition?

asked 2021-05-29

Complex number in rectangular form What is (1+2j) + (1+3j)? Your answer should contain three significant figures.

asked 2021-08-10

Graph the point \(\displaystyle{z}=\sqrt{{{3}}}-{i}\) and find the modulus and argument of z

asked 2022-01-18

If z is a complex function and \(\displaystyle{z}^{{{3}}}={8}{i}\), what are all the values of z?

asked 2022-01-17

What are complex numbers? \(\displaystyle{\ln{{\left({1}-{i}\right)}}}\)

asked 2022-01-17

Is \(\displaystyle{3}+\sqrt{{{5}}}\) a complex number?

asked 2021-12-04

Write each quotient as a complex number. \(\displaystyle{\frac{{{4}-{3}{i}}}{{-{1}-{4}{i}}}}\)