1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zimovet [89]
3 years ago
9

What is (7-7i) in polar form

Mathematics
2 answers:
KonstantinChe [14]3 years ago
7 0

The polar form of the complex number 7 - 7i is \boxed{z = 7\sqrt 2 \left( {\cos \left({\frac{{7\pi }}{4}} \right) - i\sin \left( {\frac{{7\pi }}{4}} \right)} \right)}.

Further explanation:

The complex number is z = a + ib.

The polar form of the complex number can be expressed as follows,

\boxed{z = r\left( {\cos {{\theta }} + i\sin {{\theta }}} \right)}

Here, r is the modulus of the complex number and {{\theta }} is the argument or angle of complex number.

Explanation:

The given complex number is z = 7 - 7i.

The value of a is 7 and the value of b is -7.

The value of r can be obtained as follows,

\begin{aligned}{r^2}&= {a^2} + {b^2}\\{r^2}&= {7^2} + {7^2}\\{r^2} &= 49 + 49\\r &= \sqrt {98}\\ r &= 7\sqrt 2\\\end{aligned}

The angle can be obtained as follows,

\begin{aligned}\tan {\theta }}&=\Dfrac{{\cos {{\theta }}}}{{\sin {\theta }}}}\\ &=\Dfrac{{\frac{a}{r}}}{{\Dfrac{b}{r}}}\\&= \Dfrac{{\Dfrac{7}{{7\sqrt 2 }}}}{{ - \Dfrac{7}{{7\sqrt 2 }}}} \\&=  - 1 \\ \end{aligned}

The angle lies in the fourth quadrant as value of \sin \theta is negative and value of \cos \thet a is positive.

The angle can be obtained as follows,

\begin{aligned}{\theta }}&= 2\pi- \frac{\pi }{4}\\&=\frac{{7\pi }}{4}\\\end{aligned}

The polar form of the complex number 7 - 7i is \boxed{z = 7\sqrt 2 \left( {\cos \left( {\frac{{7\pi }}{4}} \right) - i\sin \left( {\frac{{7\pi }}{4}} \right)} \right)}.

Kindly refer to the image attached.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic Sequence

Keywords: complex numbers, imaginary roots, polar form, 7-7i, general form, argument, coordinate.

jonny [76]3 years ago
4 0
 z = 7√2 cos(7/8π) + 7√2i sin(7/8π) = 7√2e^(i7/8π)
You might be interested in
Given that cos(theta) = 8/17 and that theta lies in Quadrant IV, what is the exact value of sin 2(theta)?
Deffense [45]

Answer:    -\frac{240}{289}

=========================================================

Explanation:

Use the pythagorean trig identity \sin^2(\theta)+\cos^2(\theta) = 1 and plug in the fact that \cos(\theta) = \frac{8}{17}\\\\

Isolating sine leads to \sin(\theta) = -\frac{15}{17}\\\\. I'm skipping the steps here, but let me know if you need to see them.

The result is negative because we're in quadrant 4, when y < 0 so it's when sine is negative.

Therefore,

\sin(2\theta) = 2\sin(\theta)\cos(\theta)\\\\\sin(2\theta) = 2*\left(-\frac{15}{17}\right)*\left(\frac{8}{17}\right)\\\\\sin(2\theta) = -\frac{240}{289}\\\\

6 0
1 year ago
A game has a circular playing area in which you must hit a ball into a circular hole. The area of the playing area is 16ft2. The
frez [133]

Considering the area of the hole, it is found that there is a 4.9% probability of hitting a ball into the circular hole.

<h3>What is the area of a circle?</h3>

The area of a circle of radius r is given by:

A = \pi r^2

In this problem, the hole has a diameter of 1 ft, hence it is radius is of r = 1 ft/2 = 0.5 ft, and it's area is given by:

A = \pi \times (0.5)^2 = 0.7854 \text{ft}^2

Hence the probability is given by:

p = 0.7854/16 = 0.049 = 4.9%

More can be learned about probabilities at brainly.com/question/14398287

#SPJ1

5 0
1 year ago
Need help......................
Lera25 [3.4K]
I don’t really know it sry
5 0
3 years ago
Add the following decimals​
Fantom [35]

Answer:

148.91

Step-by-step explanation:

hope it helps<333

5 0
3 years ago
Graph y=5/3x-9 in slope intercept
prisoha [69]

Answer:

Step-by-step explanation:

3 0
2 years ago
Other questions:
  • I don’t know what do do help
    8·1 answer
  • What is the meaning of the underlined digit 648? The underlined number is 4 on the question
    8·2 answers
  • Divide -3x3 - 2x2 - x - 2 by x – 2.
    9·2 answers
  • Hi guys my little brother needs help to Do his homework And I’m doing mine so I can’t help him can anyone help plzz
    15·1 answer
  • What is an equation of a line in point slope form that passes through (-2, -6) and has a slope of 1/3
    14·1 answer
  • HELP
    11·2 answers
  • HELP I NEED THIS SOLVED IN SIMPLEST FORM!!<br> 5/6 + 1/2 =
    5·2 answers
  • Which of the following is the product of the rational expressions shown<br> below?<br> 3/x+7 x 4/x
    8·2 answers
  • 6 to the negative 4th power times 6 to the 7th power ​
    7·1 answer
  • The area of a circle is 100 pie. What is the radius?<br> A 25<br> B) 10<br> C 50<br> D) 5
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!