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How To Find the Polar Form of a Complex Number

Graph showing a complex number graphed in rectangular coordinates

Polar form is a way of representing complex numbers by graphing them. But before determining how to find the polar form, we must first establish what a complex number is. A complex number is a trigonometry concept that means a “combination of real numbers and imaginary numbers.” Real numbers can be positive or negative. They are essentially any quantifiable number that, when squared, results in a positive value.

Imaginary numbers are numbers that don't compute on a calculator. When squared, they result in a negative value. Because these numbers are imaginary, they cannot be expressed with numerical values. Instead, the unit used for imaginary numbers is i, the square root of -1. Here are some examples of imaginary numbers: 5i, 3.6i, −14.3i, (√7)i, 2,891i. All of these numbers have been multiplied by the value of i or √−1.

Complex numbers have a real part and an imaginary part. Complex number z is used to represent the combined result of the real and imaginary parts. Here are some examples of complex numbers:

polar form: Example of a complex number

Example of a complex number

Example of a complex number

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How To Find the Focus of a Parabola: Your Easy Guide

how to find the focus of a parabola: Diagram of a parabola

If you want to know how to find the focus of a parabola, you first need to define what a parabola is. A parabola is a curved figure where any point on the curve is equal distance from a fixed point (called the focus) and a fixed straight line (called the directrix).

Let’s identify the parts of a parabolic function. In the graph above, you see a given line that intersects the directrix at a 90-degree angle. This straight line is called the axis of symmetry. The point that is marked C, signifying where the parabola opens, is called the vertex. The vertex is always midway between the focus and directrix of a parabola.

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Learn How To Find the Area of a Non-Right Triangle

area of a non right triangle: Diagram of a right triangle

To find the area of a non-right triangle, let’s first review the standard area formula of a right triangle. A right triangle is made up of three sides: the base, the height, and the hypotenuse. To get the area of a triangle you must multiply the two adjacent side lengths of the 90° angle, which are the base and the height of the triangle, and divide this quantity by half. This is the formula for the area of a right triangle:

Formula for the area of a right triangle

However, this formula doesn't work as effectively for acute and obtuse angles. So here's how to find the area of a non-right triangle.

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How You Use the Triangular Proportionality Theorem Every Day

Diagram showing the triangle proportionality theorem

The triangle proportionality theorem is a geometric law stating that when you draw a line parallel to one side of a triangle, it’ll intersect the other two sides of the triangle and divide them proportionally. Regardless of whether they're obtuse, acute, or right triangles, this theorem can be used to determine unknown lengths within similar triangles.

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How To Master Quadratic Regression

quadratic regression graph

Similar to functions, quadratic regression is a way to model a relationship between two sets of independent variables. Quadratic regression is the process of determining the equation of a parabola that best fits a set of data. This set of data is a given set of graph points that make up the shape of a parabola. The equation of the parabola is y = ax2 + bx + c, where a can never equal zero.

The graphs of quadratic functions have a nonlinear “U”-shape with exponential curves on either side of a single intercepting y-value. We’ll show you how to use this equation.

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