Complex numbers -- Loci Problems

jackdaw

Hi
From Engineering Mathematics KA Stroud
See link below , I am having difficulty understanding this problem,
I don't see where he makes the jump from
z + 1 = x +jy +1 = (x+1) +jy = r1Ltheta1 = z1

he is putting it in polar form here ?

and surely it should be (x+1)Squared - ySQUARED .. as jSQUARED is -1


People who have the book its 5th ed p. 468




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MathsManiac

I think you can safely ignore the polar stuff that's interspersed with the solution - my guess is that he's including the polar form along the way because sometimes when you express things in polar form the answer just jumps out at you.

Anyway, to answer your question, the modulus of a+bj is defined to be a^2 + b^2, not a^2 + (bj)^2. (It's the distance from the point to the origin on an Argand diagram.)

So, he has just expressed z as x+yj, and then found the relevant moduli in terms of x and y.

That ok?

jackdaw

MathsManiac wrote: »

I think you can safely ignore the polar stuff that's interspersed with the solution - my guess is that he's including the polar form along the way because sometimes when you express things in polar form the answer just jumps out at you.

Anyway, to answer your question, the modulus of a+bj is defined to be a^2 + b^2, not a^2 + (bj)^2. (It's the distance from the point to the origin on an Argand diagram.)

So, he has just expressed z as x+yj, and then found the relevant moduli in terms of x and y.

That ok?

Sort of... but still why is the y^2 positive, since j^2 is -1 ??

Cokehead Mother

"the modulus of a+bj is defined to be a^2 + b^2, not a^2 + (bj)^2."

So the modulus of (x + 1) + yj is root[(x + 1)^2 + y^2] and not root[(x + 1)^2 + (yj)^2] which would give you -y^2.

jackdaw

of course!!!


cheers!