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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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How To Find the Third Side of a Triangle in 3 Ways

how to find the third side of a triangle: graph of the law of sines

There are several different ways you can compute the length of the third side of a triangle. Depending on whether you need to know how to find the third side of a triangle on an isosceles triangle or a right triangle, or if you have two sides or two known angles, this article will review the formulas that you need to know.

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What Is the Domain of Tangent, Sine, and Cosine?

domain of tangent: graph of three reciprocal functions

The main three trigonometric functions are the sine function, cosine function, and tangent function, sometimes represented as sin x, cos x, and tan x. These functions measure the ratio between different sides of a triangle. The easiest way to memorize these trigonometric functions is the mnemonic device SOHCAHTOA:

Sine = Opposite over Hypotenuse

Cosine = Adjacent over Hypotenuse

Tan = Opposite over Adjacent

Understanding tangent, sine, and cosine as functions enables us to figure out the range and domain of tangent, sine, and cosine.

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Breaking Down Converse Statements, Inverse Statements

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converse statement: Table of conditional statement examples

Our everyday lives are full of logical statements, deductive reasoning, and counterexamples. In math we may call these "theorems'' or "postulates." In normal language, we see these as "then statements'' that can be assigned certain truth values. In other words, they can be true or false. Let's dive into the world of logical equivalence and review how converse statements fit in. We’ll also define inverse statements and contrapositive statements.

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