In Exercises 15–18, write each complex number in rectangular form. If necessary, round to the nearest tenth.8(cos 60° + i sin 60°)

Complex numbers are numbers that have a real part and an imaginary part, typically expressed in the form a + bi, where a is the real part and b is the coefficient of the imaginary unit i. In trigonometric form, a complex number can be represented as r(cos θ + i sin θ), where r is the magnitude and θ is the angle. Understanding how to convert between these forms is essential for solving problems involving complex numbers.

The conversion from polar to rectangular form involves using the relationships x = r cos θ and y = r sin θ, where (x, y) are the rectangular coordinates. This process allows us to express a complex number in the standard form a + bi. For the given complex number, substituting the values of r and θ will yield the rectangular coordinates necessary for the solution.

Trigonometric values such as cos(θ) and sin(θ) are fundamental in determining the components of a complex number in polar form. For example, cos(60°) equals 0.5 and sin(60°) equals √3/2. Knowing these values is crucial for accurately converting the complex number from its trigonometric representation to rectangular form.