Final answer:
To analyze a complex number, determine its real and imaginary parts directly from its components, calculate the magnitude with the Pythagorean theorem, and find the angle using the arctangent function.
Step-by-step explanation:
The question pertains to the analysis of a complex number, which would include finding its real part, imaginary part, magnitude, and angle (often referred to as the argument). To analyze a complex number written in the form A = a + ib (where i is the imaginary unit, and a and b are real constants), we follow these steps:
- The real part is simply a.
- The imaginary part is b.
- The magnitude (also called the modulus) of the complex number is calculated using the Pythagorean theorem √(a² + b²). This is analogous to finding the hypotenuse of a right triangle with sides a and b.
- The angle (or argument) is found by using the arctangent function tan⁻¹(b/a) and is usually measured in radians.
By applying these steps to the complex number provided, we can efficiently break it down into its constituent parts and better understand its properties in the complex plane.