Question

In an Argand Plane, the equation $$ (m + i)z + (m - i)\bar{z} + 2c = 0$$ represents slope intercept form of straight line where m is the slope and c is the imaginary axis intercept. Prove it. Also show that if a and b are intercepts of a straight line on real and imaginary axes respectively, then its equation is $$(b - ai)z + (b + ai)\bar{z} = 2ab$$

Answer 1

So z can be any complex number, maybe you should represent it by z=u+vi or z=r*e^{i theta} instead? I'll work through this and see what I can figure out. Try to share whatever you're thinking.

Answer 2

I am just blank with this question. :P

Answer 3

z=x+i y mm its variable not constant

Answer 4

Here, I'll introduce you to what algebra looks like with complex numbers.

First, let's represent z as a sum of two numbers where u and v are real numbers only. So:
\[\Large z= u+iv\] and that means its complex conjugate is \[\Large \bar z = u - iv\]

We can plainly see that adding the complex conjugate or subtracting the complex conjugate from the original number gives us either an entirely real or imaginary part:

\[\Large z+\bar z = u+iv + u -iv = 2u = 2\Re(z) \]
\[\Large z - \bar z = u+iv - u +iv =2iv=2i \Im(z)\]

Remember the argand diagram is really just a fancy way of saying "xy-plane" except you're labelling the x-axis as the real direction and y-axis the imaginary direction. So this means the imaginary part is your y value and your real part is your x value of the classic linear equation we all know and love, y=mx+b

Answer 5

its the same to the real , convert the equation to the standerd equation mmm

i y = a x + C mmm wait lemme chek from this

Answer 6

understood it till here :)

Answer 7

Ok, so now see if you can use these little identities I have laid out for you by distributing and factoring out the m and i on the z terms. Play with it a little and I'll help you if you get stuck.

Answer 8

I will try for the rest

Thank you :)

Answer 9

Remember, since you are looking for an equivalent formula to y=mx+b you should get something like: \[\LARGE \Im(z)=m \Re(z)+c\] since these are exactly the analogous parts yeah? =)