Question

Find the principal argument of (√3+i)²⁰²⁰.

Answer 1

To find the principal argument of (√3+i)²⁰²⁰, first find the argument of (√3+i) and then multiply it by 2020. The argument of a complex number is the angle it makes with the positive real axis in the complex plane.

Step-by-step explanation:

To find the principal argument of (√3+i)²⁰²⁰, we need to first find the argument of (√3+i) and then multiply it by 2020. The argument of a complex number is the angle it makes with the positive real axis in the complex plane.

Let's start by finding the argument of (√3+i). We can represent (√3+i) as a complex number in the form a + bi, where a = √3 and b = 1. To find the argument, we can use the inverse tangent function, arctan(b/a).

The principal argument of (√3+i) is arctan(1/√3) = π/6.

Now, we can multiply the principal argument by 2020 to find the principal argument of (√3+i)²⁰²⁰. π/6 * 2020 = 1010π.