Mathematics, 22.12.2020 09:00 jeffreyaxtell4039

Given z^2=1/2(cos(2pi/5)+i sin(2pi/5)), which lettered point represents z?

Answers: 1

Show answers

Answers

Answer from: chrismed2001

is represented by point A.

Step-by-step explanation:

According to the De Moivre's Formula, the power of a complex number of the form $z = r\cdot (\cos \theta + i\,\sin \theta)$ is defined by this formula:

$z^{n} = r^{n}\cdot [\cos n\theta + i\,\sin n\theta]$ (1)

Where:

- Norm of the complex number, dimensionless.

$\theta$ - Direction of the complex number, measured in radians.

- Power of the resulting complex number, dimensionless.

Given that $z^{2} = \frac{1}{2}\cdot \left[\cos \left(\frac{2\pi}{5} \right)+ i\,\sin \left(\frac{2\pi}{5} \right)\right]$ , then the following variables are:

$r^{2} = \frac{1}{2}$ (2)

$2\theta = \frac{2\pi}{5}$ (3)

And the norm and direction of the complex number are, respectively:

$r = \frac{\sqrt{2}}{2}$ and $\theta = \frac{\pi}{5}$

Then, the complex number is:

$z = \frac{\sqrt{2}}{2}\cdot \left[\cos \left(\frac{\pi}{5} \right)+i\,\sin \left(\frac{\pi}{5} \right)\right]$

$z = 0.572 + i\,0.416$

Which corresponds to point A.

Answer from: Quest

there are no figures how am i supposed to answer this question

step-by-step explanation:

Answer from: Quest

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights

Another question on Mathematics

Mathematics, 21.06.2019 19:50

Which statement is true? n is a point of tangency on circle p. pt is a secant of circle p. is a secant of circle p. vu is a tangent of circle p.

Answers: 3

Answer

Mathematics, 21.06.2019 20:10

What additional information could be used to prove abc =mqr using sas? check all that apply.

Answers: 1

Answer

Mathematics, 21.06.2019 21:50

If you double the input of a function and it results in half the output, and if you triple the input and it results in a third of the output, what can be guessed about the function? check all that apply.

Answers: 3

Answer

Mathematics, 22.06.2019 09:30

Over which interval does the growth rate of the exponential function for us to exceed the growth rate of the linear function