Where z is a complex number, what is the cartesian form of |Z-2+3i| = 1?
Z is simply a general complex number, which can be written as Z = x+iyHere |Z-2+3i| = 1 can be written as |Z-(2-3i)| = 1, which is just an expression for every Z whose distance from the point (2,-3i) is equal to 1.We can solve this by recalling that Z = x+iy, and so we can seperate the real and imaginary parts in the modulus function. i.e. 1 = |(x-2) + i(y+3)| Evaluating the modulus now becomes simple as we calculate the magnitude using pythagoras. This Yields:12 = (x-2)2 + (y+3)2 , which is the cartesian form!we recognise this as the equation of a circle, with centre (2,-3) and radius 1.
MH
Related Maths A Level answers
All answers ▸3. The point P lies on the curve with equation y=ln(x/3) The x-coordinate of P is 3. Find an equation of the normal to the curve at the point P in the form y = ax + b, where a and b are constants.
Show that sin2A is equal to 2sinAcosA
A curve C has the equation x^3 + 2xy- x - y^3 -20 = 0. Find dy/dx in terms of x and y.
Solve the simultaneous equations y+4x+1 = 0 and y^2+5x^2+2x = 0