Question

Sketch in the argand plane:
-2+4i+5....

I know how to do the argand diagram but I am confused about the +5.

Any assistance is appreciated.
Kind regards....

Answer 1

\[-2+4i+5\]

Answer 2

whats an argand plane?

Answer 3

it is a plane which has points from real and complex numbers

Answer 4

similar to a cartesian plane

Answer 5

if thats just the complex plane, then combine like terms

Answer 6

-2+4i+5 = 3+4i

Answer 7

right..
now this comes from a problem which states :

show that the set of complex numbers z which satisfy |z| = |z-1+2i|

Answer 8

is a line in the argand plane.

Answer 9

|z| represents distance from the origin right?

Answer 10

so the first thing i did was let z=a+bi

Answer 11

and the did the calculations

Answer 12

so i was left with -2a+4b+5

Answer 13

I know this as the Gaussian Plane (-: Interesting actually.

Answer 14

But if you want to draw a complex number in the Argand Plane you need an argument then and a magnitude.

Answer 15

now a is the real part and b imaginary
so i rewrote the term as -2 + 4i +5

Answer 16

you could do it with the cartesian form as well ..space....real no. goes on the hor line and imaginary on the verical

Answer 17

a+bi = a+bi - 1 + 2i

a+bi = (a-1) +(b+2)i

0 = (a-1)-a +(b+2)i-bi

0 = -1+2i , not sure if its right, but this is what i end up with

Answer 18

but remember the modulus |z|
so when you stick a+bi into that, you left with |a+bi|
and then you have to take the sqrt of the squares of a + b

Answer 19

so |a+bi| = |a+bi-1+2i|

Answer 20

http://www.wolframalpha.com/input/?i=%7Cz%7C+%3D+%7Cz-1%2B2i%7C

i think the wolf agrees .... but i cant be sure lol

Answer 21

to solve that you have to square the terms then take sqrt

Answer 22

wolf agrees. but there is no imaginary part?

Answer 23

|z| is a distance from the origin such that

|z| = sqrt(a^2+b^2) , z=a+bi

Answer 24

yes

Answer 25

as in thereom of pythagoros

Answer 26

what about the RHS

Answer 27

check this : http://www.wolframalpha.com/input/?i=%7Ca%2Bbi%7C+%3D+%7Ca%2Bbi-1%2B2i%7C

Answer 28

a^2+b^2 = (a-1)^2 + (b+2)^2

a^2+b^2 = a^2 -2a +1 + b^2 +4b +4

0 = -2a +1+4b +4

2a -4b = 5

looks linear to me

Answer 29

if we assume a convention xy plane as the rc plane; a=r, b=c

Answer 30

even -2a+4b+5

now a is real part, b is imaginary

Answer 31

b is the real coeff of the imaginary part, yes

Answer 32

hence the term is -2+4i+5
Should I then just add the -2 and 5 ?

Answer 33

b is not "the imaginary part" it is a real coefficient OF the i part

Answer 34

okay , that makes sense...

Answer 35

think of b as the y axis; and a as the x axis

Answer 36

the i part is just a unit measure along the "b" axis then

Answer 37

okay

Answer 38

@unseenoceans, was this question about something like this?



Discussion of complex functions ?