For z a complex number, arg (z) is the angle the line from 0 to z, in the complex plane makes with the real axis. "arg(w + 1) = α a r g ( w + 1) = α means that w lies on thine through the origin has slope tan(α) t a n ( α) so, writing z= x+ iy, has equation y = tan(α)x y = t a n ( α) x. You want the value of z= x+ iy satisfying (x − 3)2 The argument of a complex number is the anti-clockwise angle that it makes when starting at the positive real axis on an Argand diagram. This involves using the tan ratio plus a sketch to decide whether it is positive/negative and acute/obtuse. Negative arguments are for complex numbers in the third and fourth quadrants. The "intuitive" reason you seek, is that any complex number $z$ can be written in function of its argument $\theta$ as follows: $$z = re^{i\theta},$$ where $r$ is the I first simplified the complex number arg[z−1 z+1] arg [ z − 1 z + 1] by substituting z = x + iy z = x + i y and obtained the complex number. Then I used the formulae tan(θ) = I(z)/R(z) tan ( θ) = ℑ ( z) / ℜ ( z) but my doubt is whether we have to check quadrants for the obtained angle or not. I am confused as it is given argument 1. in your solution, you find, correctly, a and b such that 3 + 4i 1 − i + 2 − i 2 + 3i = a + bi. but you need to find the modulus and the argument of the number. That is, you need to find r > 0 and θ ∈ [0, 2π) such that. 3 + 4i 1 − i + 2 − i 2 + 3i = r(cosθ + isinθ). Take a look at the rightmost figure at the bottom (the leftmost figure will be used at the end of this answer).. Let us concentrate on the blue circles. Their common property : all of them pass through 2 fixed points on the x-axis that are $(-2,0)$ and $(2,0)$. .

what is arg z of complex number