Final answer:
The question requires converting a rectangular form complex number to polar form by understanding the polar coordinate system, using the Pythagorean theorem for magnitude, and inverse tangent function for the angle. The polar forms are then added to find the final magnitude and angle.
Step-by-step explanation:
The given question involves converting a complex number from rectangular form to polar form. Let's break down the given complex number: 3∠30°(6−j8 +3∠60°(2+ j)). First, we need to understand the polar coordinate system and how to represent complex numbers within this system. The polar form of a complex number is represented as r∠θ, where r is the magnitude and θ (theta) is the angle made with the positive real axis.
Initially, we have the complex number 3∠30°. In polar coordinates, this is equivalent to a magnitude of 3 and an angle of 30°. The complex number 6−j8 can be converted to polar form using Pythagorean theorem for the magnitude and inverse tangent function for the angle. Similarly, 3∠60°(2+ j) represents the multiplication of two polar forms, which requires us to multiply their magnitudes and add their angles.
The polar form of the complex number can then be found by adding the two complex numbers in polar form. The final polar form will have the combined magnitude, computed using vector addition principles, and the angle that is the resultant direction.