Complex No. (3 Viewers)

[Aysce]

Can someone help me do :

Solve the equation:



Forgot how to do it.. thanks

 

[Drongoski]

Can someone help me do :

Solve the equation:



Forgot how to do it.. thanks

1 way - use the quadratic formula





Another way: completion of the square

 

[Hermes1]

Can someone help me do :

Solve the equation:



Forgot how to do it.. thanks

use the quadratic formula and for the root part you will hav to solve separately. in exams they usually get u to find the square root part first.

 

[ohexploitable]

or by inspection you can immediately see z=1 is a soln

then sum of roots: z+1=-i, .'. other root is z=-i-1

 

[Hermes1]

or by inspection you can immediately see z=1 is a soln

then sum of roots: z+1=-i, .'. other root is z=-i-1

lol that would be a one in a million chance to get a question like this with 1 as a solution in an exam.

 

[Aysce]

Ah thanks guys ^^. Kinda derped for a moment there

 

[Drongoski]

or by inspection you can immediately see z=1 is a soln

then sum of roots: z+1=-i, .'. other root is z=-i-1

Brilliantly simple; this simple mind didn't see that.

 

[funnytomato]

Can someone help me do :

Solve the equation:



Forgot how to do it.. thanks

z^2-1 + i (z-1) = 0
(z+1)(z-1) + i (z-1) = 0
(z+1+i) (z-1) =0

 

[Drongoski]

z^2-1 + i (z-1) = 0
(z+1)(z-1) + i (z-1) = 0
(z+1+i) (z-1) =0

Very nice too. Very manipulative of you.

 

[Aysce]

Umm, my tutor moved on to like the argand diagram but I don't get that when I found the argument of a certain question, I had to subtract or add 180 degrees. For example, Express -1-i in mod-arg, i got the arg as 45 degrees but I had to subtract 180 degrees? If anyone can explain the quadrants and why I'd highly appreciate it ^^

 

[AAEldar]

Umm, my tutor moved on to like the argand diagram but I don't get that when I found the argument of a certain question, I had to subtract or add 180 degrees. For example, Express -1-i in mod-arg, i got the arg as 45 degrees but I had to subtract 180 degrees? If anyone can explain the quadrants and why I'd highly appreciate it ^^

Picture where would lie on the Argand diagram. -1 would mean you go to the left of the Origin one unit, and means you go below the origin by one unit. This puts the coordinate in the 3rd quadrant, and since you go from you get the Argument as being , which can be simplified.

 

[Shadowdude]

Pro-tip: Always draw a picture.

 

[Hermes1]

Pro-tip: Always draw a picture.

mate im sorry but ur pro-tips shuld be called fukin obvious-tips.

 

[Alkanes]

^ lol

 

[Shadowdude]

mate im sorry but ur pro-tips shuld be called fukin obvious-tips.

Yeah but Protip sounds nicer. I'm also in the processes of copyrighting the term... so I should use it as much as possible. =P

 

[Aysce]

Picture where would lie on the Argand diagram. -1 would mean you go to the left of the Origin one unit, and means you go below the origin by one unit. This puts the coordinate in the 3rd quadrant, and since you go from you get the Argument as being , which can be simplified.

Umm sorry but I still don't really understand, like I know that the point is in the 3rd quadrant, but I don't completely understand what you did after that.

 

[Alkanes]

For now, just know how to do it, no need to understand haha. Even myself who has just started this don't understand why you subtract 180 etc, but i think its got to do something with the revolution of the circle on the point etc.

 

[Aysce]

Eh i'll probably understand once it's done at school T.T

 

[nightweaver066]

Umm sorry but I still don't really understand, like I know that the point is in the 3rd quadrant, but I don't completely understand what you did after that.

What he/she means is that you always take an angle between the range that would satisfy the complex number.

Using z = -1 - i, plotting it on the Argand diagram would place it in the 3rd quadrant and so you want the argument to be in the range and to be in the 3rd quadrant.

So finding it would be tanR = 1
R = pi/4

For it to be in the 3rd quadrant and to satisfy the range, it must be

Hopefully what i said was correct and helps you.

 

[Aysce]

Yeah I understand it a little better now, but is there like some type of rule that is similar to ASTC? I mean I've done a few questions, and I've found out that when it's in the 2nd quadrant you add 180 and in the 3rd you subtract 180. While if the point is in the 1st or 4th quadrant, the answer stays the same - No need to subtract or add 180.