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Find the distance and midpoint of complex numbers

Trigonometry: Master Angles, Functions & Applications

Imaginary and Complex Numbers

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Introduction to imaginary numbers

Complex numbers and complex planes

Adding and subtracting complex numbers

Complex conjugates

Complex Conjugates

Multiplying and dividing complex numbers

Distance and midpoint of complex numbers

Angle and absolute value of complex numbers

Polar form of complex numbers

Operations on complex numbers in polar form

Inverse Trigonometric Functions

Finding inverse trigonometric function from its graph

Evaluating inverse trigonometric functions

Finding inverse reciprocal trigonometric function from its graph

Finding exact value of inverse reciprocal trig functions

Inverse Reciprocal Trigonometric Function: Finding the Exact Value

Inverse reciprocal trigonometric function: finding the exact value

Bearings

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

Trigonometric Ratios and Angle Measure

Unit circle

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

ASTC rule in trigonometry (All Students Take Calculus)

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

Graphing Trigonometric Functions

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

Applications of Trigonometric Functions

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

Trigonometric Identities

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Cofunction identities

Solving Trigonometric Equations

Solving first degree trigonometric equations

Solving second degree trigonometric equations

Solving trigonometric equations involving multiple angles

Determining non-permissible values for trig expressions

Solving trigonometric equations using pythagorean identities

Solving trigonometric equations using Pythagorean identities

Solving trigonometric equations using sum and difference identities

Solving trigonometric equations using double-angle identities

Right Triangle Trigonometry

Use sine ratio to calculate angles and sides (Sin = \(  \frac{o}{h}\) )

Use cosine ratio to calculate angles and sides (Cos =  \(  \frac{a}{h}\)  )

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles 

Use tangent ratio to calculate angles and sides (Tan =  \(  \frac{o}{a}\)  )

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Ex.1

Ex.2

Finding the distance between two complex numbers using the distance formula

Finding the midpoint between two complex numbers

Finding the distance between a complex number and its conjugate

Midpoint between a complex number and its conjugate

We know how to find the distance and the midpoint between two points on a <a href='[[glossary.html|{"keyword":"Cartesian Plane","term":"Cartesian Plane"}]]'>Cartesian plane</a>, but what if we are dealing with a complex plane? It turns out that the formulas that are used to find the distance and the midpoint between two complex numbers are very similar to the formulas we use for the Cartesian points. In this section, we will learn how to use the midpoint formula and the distance formula for Complex numbers.

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Distance and midpoint of complex numbers

What You'll Learn

Apply the distance formula to find the separation between two complex numbers on the complex plane

Use the midpoint formula to locate the point exactly halfway between two complex numbers

Recognize that complex plane distance formulas mirror Cartesian plane formulas with real and imaginary axes

Calculate distances and midpoints for complex conjugates and identify their geometric properties

What You'll Practice

Finding distances between complex numbers using real and imaginary parts

Calculating midpoints by averaging real parts and imaginary parts separately

Working with complex conjugates to find distance and midpoint

Simplifying expressions involving squared differences of complex components

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

4 Video lessons

Practice exercises

Skills

Complex Numbers

Distance Formula

Midpoint Formula

Complex Plane

Complex Conjugates

Pythagorean Theorem