When multiplying a number by its conjugate you should end up with a real number. You can check which 2 complex numbers, multiplied, give you a real number. Let's start with your school's answer. If you do (7-5i)*(-7+5i), you get 49 +70i-25i^2. This, in simplified form, is equal to 74+70i, which is a complex number, not a real number. Usually we have two methods to find the argument of a complex number. (i) Using the formula θ = tan−1 y/x. here x and y are real and imaginary part of the complex number respectively. This formula is applicable only if x and y are positive. But the following method is used to find the argument of any complex number. A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1. The number a is called the real part of the complex number, and the number bi is called the imaginary part. Complex numbers are the points on the plane, expressed as ordered pairs (a, b), where a represents the coordinate for the horizontal axis and b represents the coordinate for the vertical axis. Let's consider the number − 2 + 3i. The real part of the complex number is−2 and the imaginary part is 3i. Find the modulus and argument of the complex number {eq}z = -2 -2 i {/eq}. Step 1: Graph the complex number to see where it falls in the complex plane. This will be needed when determining the 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 But as. z(r, θ) = z(r, θ + 2kπ), z ( r, θ) = z ( r, θ + 2 k π), so the right part can be positive or negative, while the left part does not change sign. There are no solutions for the case r ≠ 1 r ≠ 1. So. zz = z ⇒ z = ±1, z z = z ⇒ z = ± 1, as the only solutions. Share. mTpC.

what is arg z of complex number