= ― and = + Use trigonometric forms to find
and /

The given complex numbers are  -

z1 = 5√2(cos(3π/4) +isin(3π/4))

z2 = 5√2(cos(π/4)   + isin(π/4))

The product of z1 and z2 is  -

z1z2 = 50(cos(π) + isin(π)) is -50

The quotient of z1 and z2 is  -

z1/z2 = cos(π/2) + isin(π/2)  is  i

To simplify the   expression,we begin by rearranging the terms. We move the minus sign from the numerator to the front and divide both the numerator and denominator   by 5. This   gives us   -(1-i)/(1+i).

Next,  we multiply both the   numerator and denominatorby 1-i to eliminate the complex number in the denominator. This results in 1(1-i)²/2.

Expanding   the numerator,we get a quadratic expression in the form a+bi. It's important to remember to bring along the 2 in the denominator while simplifying.

That is

z1 = 5√2(cos3π/4 + isin3π/4); z2 = 5√2(cosπ/4 + isinπ/4).

z1z2 = 50(cosπ + isinπ) = - 50

z1/z2 = cosπ/2 + isinπ/2 = i

Learn more about Trigonometric forms:
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Full Question

Use trigonometric forms to find z1z2 and z1/z2. (Enter your answers in the form a + bi.)

z1 = −5 + 5i,    z2 = 5 + 5i

z1z2= ?

z1/z2= ?

Now you can submit the work you have finished from the "Explore: Topic of Personal Interest" assignment here. Type your response directly into the space provided.

Assignment:

You will have extended time to complete this assignment. When you are ready to submit, find the "Explore Submission: Topic of Personal Interest" link located in your Course Map.

Using Spanish resources (internet, newspapers, magazines, books), write a minimum of 5 sentences in Spanish about a topic of personal interest. For example, if you are a soccer fan, you may consider researching information on a national soccer team or a famous soccer player from a Spanish-speaking country. Other topics to consider: national sport, national food, special event, or location (museum, temple, rainforest). When researching, think about what makes this specific person, place or event noteworthy or interesting to write about.

Be sure to cite your resources at the end of your paragraph.



Example:

Los guaraníes son una gente indígena de Paraguay. Practican una forma de tejer¹ se llama Ñandutí. Crean muchas artesanías a mano con los tejidos². El estilo de ñandutí es como una telaraña³. El arte guaraní representa flores, animales, y símbolos de la naturaleza.

¹tejer: to weave, knit
²tejidos: fabrics, textiles
³telaraña: spider web



Historia del tejido Ñandutí
https://www.nodalcultura.am/2018/04/historia-del-tejido-nanduti/



You will be graded on (a) appropriate use of grammar and vocabulary, (b) completeness and detail of the response, and (c) overall quality of the response.

Use outside sources (Internet, books, magazines, etc.) to gather information for this assignment. However, be sure not to copy the information directly from those sources. Copying information and presenting it as your own work is considered plagiarism and will result in a failing grade. You need to rephrase the information into your own words and cite the source of the information you used. This means to reference where your research came from- include the link to the article or webpage.

Cuales géneros literarios aparecen en el evangelio de mateo

Change this verb from the present tense to the preterite tense.
Ustedes lavan

Answer for Blank 1:

The direct approach to organize negative news messages should be used when __________.
A.the situation is routine or minor
B.the blow of the negative news is to be softened
C.the reader has an emotional investment in the situation
D.a need to maintain a close working relationship with the reader arises
E.the news is expected to come as a shock to the reader

Computers (part 1) Review and Quiz Part 2
Explore Submission: Topic of Personal Interest Active
Prompt
Here you will submit your completed work from the activity, "Explore: Topic of Personal Interest." Type or copy/paste your
response directly into the space provided.
Use Spanish resources (internet, newspapers, magazines, books), to write 1-2 paragraphs in English about a topic of
personal interest. For example, if you are a soccer fan, you may consider researching information on Spain's national soccer
team or a famous soccer player from a Spanish-speaking country.
Use outside sources (Internet, books, magazines, etc.) to gather information for this assignment. However, be sure not to
copy the information directly from those sources. Copying information and presenting it as your own work is considered
plagiarism and will result in a failing grade. You will need to rephrase the information into your own words and cite the source
of the information you used.

Prompt
Here you will submit your completed work from the activity, "Explore: Topic of Personal Interest." Type or copy/paste your
response directly into the space provided.
Use Spanish resources (internet, newspapers, magazines, books), to write 1-2 paragraphs in English about a topic of
personal interest. For example, if you are a soccer fan, you may consider researching information on Spain's national soccer
team or a famous soccer player from a Spanish-speaking country.
Use outside sources (Internet, books, magazines, etc.) to gather information for this assignment. However, be sure not to
copy the information directly from those sources. Copying information and presenting it as your own work is considered
plagiarism and will result in a failing grade. You will need to rephrase the information into your own words and cite the source
of the information you used.

listen to the audio and then answer the following question. feel free to listen to the audio as many times as necessary before answering the question.
how many children are in the speakers family?
uno
dos
tres
cuatro

SPANISH HELP!!

Choose the correct conjugation of the verb hacer.

1: you (tú) have tried
___ probado.
a. he
b: has
c. ha
d. hemos
e: habéis
f: han

2: Juan has eaten
___ combo.
a. he
b. has
c. ha
d. hamos
e: habéis
f: han

3. We have read
___ leído
a. he
b. has
c. ha
d. hamos
e: habéis

4. you-all (vosotros) have seen
___ visto
a. he
b. has
c. ha
d. hamos
e: habéis

5. You all (ustedes) have said
___ dicho
a. he
b. has
c. ha
d. hamos
e: habéis

6. They have left
___ salido
a. he
b. has
c. ha
d. hamos
e: habéis

7. Juan and Maria have been
___ estado
a. he
b. has
c. ha
d. hamos
e: habéis

8. I have eaten lunch
___ almorzado
a. he
b. has
c. ha
d. hamos
e: habéis

9. we have listened to
___ escuchado

10. she has washed
___ lavado
a. he
b. has
c. ha
d. hamos
e: habéis

Complete the following sentences:
1: Have the children already left? (salir)
Han ___ ya los niños.

2. I have paid the bill (pagar)
Yo ___ pagado la cuenta.

3. You have spoken with Richard. (hablar)
Tú ___ con Ricardo

4. Arsenio has been here for two hours. (estar)
Arsenio ha ____ aqui por dos horas.

5. Hasn't the baby eaten anything? (comer)
¿El bebé no ha ____ nada todavía.

6. Why haven't you-all opened the windows? (abrir)
Por qué no ____ Uds. la ventana?

7. The boy has taken out the trash (sacar)
El niño __ sacado la basura.

8. The girl has broken the dishes. (romper)
La niña ha ___ los platos.

9. They have arrived. (llegar)
Ellos ____.

10. The women have gone shopping. (ir)
Las mujeres ___ ido de compras.

how do you say “i am” in spanish

Cual es la intención del texto “el minotauro”?

SPANISH HELP!!

Complete the paragraph by using the correct past participle of the verb in parenthesis.

Fill in the blank in the following sentence with the appropriate verb in the conditional tense.

Elena ________ francés para viajar a Francia.

In a short Spanish paragraph, describe where you want to go on vacation. Why do you want to go there? What are you
going to do there? Who do you want to go with you? Your paragraph should be 4-5 sentences in length.
You will be graded on (a) application of grammar concepts learned this semester, (b) vocabulary usage, and (c) overall
quality and correctness of each sentence.