Question

Write 2 - 7i in polar coordinates on the complex plane

Answer 1

TJ , you are here, help him, please

Answer 2

Write 2 - 7i in polar coordinates on the complex plane.

Answer 3

I came here to watch you, @Hoa :/
Anyway, @Escobar12
to get the polar coordinates of a complex number in rectangular (a + bi)
form, you need two numbers, \(r\) and \(\theta\)

Use these equations
\[\huge r = \sqrt{a^2+b^2}\]\[\huge \tan (\theta) = \frac{b}a\]

Answer 4

ok thank you!

Answer 5

@Escobar12 waaaha, you are tooooo fast . I didn't get what he mean yet
@terenzreignz you know that I cannot work under that pressure, teasing me???

Answer 6

I'm not yet quite finished, @Escobar12
Once you get these two numbers, write like this...
\[\huge a+bi = r[\cos(\theta) +i\sin(\theta)]\]

Answer 7

continue TJ , it's not easy, give him more explanation, please.

Answer 8

Okay, an example...
\[\huge 1 + i\sqrt3\]
To get r, we use the formula
\[\huge r = \sqrt{1^2+(\sqrt3)^2}=\sqrt{1+3}=\sqrt4=2\]\[\huge \tan(\theta) =\frac{\sqrt3}{1}=\sqrt3\\\ \huge \theta = 60^o \left(or \quad \theta = \frac{\pi}
{3}\right)\]

so finally, we get.
\[\huge 1+i\sqrt3=2\left[\cos\left(\frac{\pi}{3}\right)+i\sin\left(\frac{\pi}{3}\right)\right]\]

Answer 9

ooohkay so what if i use the numbers to
Find (1 + i)8 using DeMoivre's Theorem

Answer 10

First, put 1+i in polar form.

Answer 11

and i use the first equation you gave me right?

Answer 12

@terenzreignz knock, knock
@Escobar12 do your stuff, no need to wait for confirmation. he will check yours then

Answer 13

I'm here. And yes, @Escobar12 Go ahead and use the equations I gave you :)

Answer 14

@terenzreignz let me take it over, ok, and you must go, I will call you back to check, ok?

Answer 15

@ Escoba12, tell me what part you cannot see the link?

Answer 16

Aching for some adventure, @Hoa ?
Okay then :D

Answer 17

\[\huge a+bi = r[\cos(\theta) +i\sin(\theta)\]\It's the formula you need to transpose from complex to polar. yours is 2 -7i, it means your a = 2, your b = -7
got it? and from right hand side, the easier way to get is = rcos (theta) + r *i *sin(theta)

Answer 18

now, balance both side, real part from LHS = real part from RHS. what does it mean?
It means 2 = r cos theta.

Answer 19

got it? the imaginary part is the same, you have -7i = r i sin(theta)
that means -7 = r sin (theta)
you have 2 new equations, 2 variables r and theta, solve for them to get r, and theta.
then put them into the polar plane.

Answer 20

ha!!! I'm out of battery.!!!

Answer 21

thanks for being very helpful(:

Answer 22

@terenzreignz back here

Answer 23

@Mertsj please, rescue.

Answer 24

i have to go now, let other help

Answer 25

Looks good to me. In summary
1. Draw a picture

2. Use the Pythagorean Theorem to find the hypotenuse (polar radius)
3. Use the tangent function to find the angle theta
4. Put the newly discovered information into the polar form of a complex number which is
\[r(\cos \theta +i \theta \sin \theta)\]

Answer 26

Sorry for my late arrival... Lag...

Answer 27

so the answer in polar form is \[\sqrt{i}\]=(cos(pi/2+i sin(pi/2))^1/2