it's ##|{\bf z}| < 3## as in the problem description.BvU said:Hello Trew,
You can't write ##{\bf z} < 3## for a complex number ...
The latter is inside the circle in the ##\bf z ## plane -- as in your notes
But the exercise asks for the image (the complex 'range') of the function (transformation), so, as you suspect, in the ##\bf w## plane.
Complex numbers are numbers that contain both a real part and an imaginary part. They are usually written in the form a + bi, where a is the real part and bi is the imaginary part, and i is the imaginary unit.
To add or subtract complex numbers, you simply add or subtract the real parts and the imaginary parts separately. For example, (3 + 2i) + (5 + 4i) = (3 + 5) + (2i + 4i) = 8 + 6i.
The conjugate of a complex number is a number with the same real part but the opposite sign of the imaginary part. For example, the conjugate of 3 + 2i is 3 - 2i.
To multiply complex numbers, you use the FOIL method, just like you would with binomials. For example, (3 + 2i)(5 + 4i) = 15 + 12i + 10i + 8i^2 = 15 + 22i - 8 = 7 + 22i.
The modulus of a complex number is the distance of the number from the origin on the complex plane. It is calculated by taking the square root of the sum of the squares of the real and imaginary parts. For example, the modulus of 3 + 4i is √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
