Complex numbers thing?

1 ⤊

Complex numbers thing?

Hey just a little complex number job I'm stuck on:

By putting z in the form x + iy and using l z l (modulus) = square root(x^2 + y^2), Find the cartesian equation of the region defined by:

(modulus) l z - (2 + 3i) l = 4

2007-10-14 22:43:04 · 3 answers · asked by trussell_47 1 in Science & Mathematics ➔ Mathematics

3 answers

l z - (2 + 3i) l = 4
l x + iy - (2 + 3i) l = 4
l (x-2) + i(y-3) l = 4
(x-2)^2 + (y-3)^2 = 16
A circle with radius = 4 and center (2, 3)

2007-10-14 23:00:51 · answer #1 · answered by Anonymous · 0⤊ 1⤋

|z - (2+3i)| =4
|x+iy - (2+ 3i)| = 4
(x-2)^2 + (y-3)^2 = 16

2007-10-14 23:06:55 · answer #2 · answered by Ivan D 5 · 0⤊ 2⤋

| x + i y - 2 - 3 i | = 4
| (x - 2) + (y - 3) i | = 4
(x - 2) Â² + (y - 3) Â² = 16

2007-10-14 23:03:06 · answer #3 · answered by Como 7 · 1⤊ 1⤋