Here are the essential concepts you must grasp in order to answer the question correctly.
Complex Numbers
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 imaginary part. 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.
Recommended video:
Polar to Rectangular Conversion
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, we will calculate the cosine and sine of the angle and multiply by the magnitude to find the rectangular coordinates.
Recommended video:
Convert Points from Polar to Rectangular
Trigonometric Functions
Trigonometric functions, such as sine and cosine, are fundamental in determining the coordinates of points on the unit circle. These functions relate angles to ratios of sides in right triangles and are periodic in nature. In the context of complex numbers, they help in finding the real and imaginary parts when converting from polar to rectangular form, especially when dealing with angles measured in degrees.
Recommended video:
Introduction to Trigonometric Functions