For the complex number z = Negative StartFraction StartRoot 21 EndRoot Over 2 EndFraction minus StartFraction StartRoot 7 EndRoot Over 2 EndFraction i, what is arg(z)? 150° 210° 240° 330° From the second equation we have y = 2 x y = 2 x. Putting this into the first equation we obtain. x2 − 4 x2 = 3. x 2 − 4 x 2 = 3. Multiplying through by x2 x 2, then setting z =x2 z = x 2 we obtain the quadratic equation. z2 − 3z − 4 = 0 z 2 − 3 z − 4 = 0. which we can easily solve to obtain z = 4 z = 4. but when imaging the z = −1 + i number on the complex plane, you see that your number is in the second quadrant. Thus, as you can see it on the picture below, the answer will be π − π/4 and not just −π/4. Note that the function f(x) = arctan(x) will always give you a single value. For instance, arctan(−1) π/4 is always true. The principal value of a complex number is usually accepted as having argument in $\;[0,2\pi)\;$ Share. Cite. Follow answered Aug 5, 2020 at 20:51. DonAntonio DonAntonio. 211k 17 17 If we consider $\arg(z^u)=\big(d\ln(r)+c(\theta+2k\pi)\big)\bigg|_{k\in\mathbb Z} In this tutorial video, you will be learning how to solve complex number from new Casio 570EX calculator. With all the step by step guides, you can easily ma Definition 1.2.10: The Principle Argument Arg : For any complex number z 0 we define the principle argument or Arg(z) as the angle which the vector z makes with the positive (real) x-axis and for which -< Arg(z) In other words, a non-zero complex number has many arguments, but only one principle argument. To find a principle argument we use the 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 stays the same if real numbers replaced with complex ones. I.e., (z1 +z2)3 = z3 1 +3z 2 1z2 +3z1z 2 2 +z 3 2 is true for any complex z1,z2. Before finally turning to the geometric interpretation of complex numbers I would like to state as an exercise the properties of conjugate numbers: Problem 2.1. Show that for any z,w ∈ C z ±w = ¯z ±w Definition: Complex Log Function. The function is defined as. log(z) = log( | z |) + iarg(z), where log( | z |) is the usual natural logarithm of a positive real number. Remarks. Since arg(z) has infinitely many possible values, so does log(z). log(0) is not defined. The angle θis called the argument of the complex number z. Notation: argz= θ. The argument is defined in an ambiguous way: it is only defined up to a multiple of 2π. E.g. the argument of −1 could be π, or −π, or 3π, or, etc. In general one says arg(−1) = π+ 2kπ, where kmay be any integer. neLc.