Imaginary
Navigation menu
By taking multiples of this imaginary unit, we can create infinitely many more pure imaginary numbers. Taking the squares of these numbers sheds some light on how they relate to the real numbers.
Imaginary can refer to: Imaginary (sociology), a concept in sociology; The Imaginary (psychoanalysis), a concept by Jacques Lacan; Imaginary number. IMAGINARY is your place for open and interactive mathematics. Join a worldwide community of math enthusiasts! PROGRAMS. experiment with interactive.
Let's investigate this by squaring the number 3 i 3i 3 i. The properties of integer exponents remain the same, so we can square 3 i 3i 3 i just as we'd imagine. In this way, we can see that pure imaginary numbers are the square roots of negative numbers! Simplifying pure imaginary numbers. The table below shows examples of pure imaginary numbers in both unsimplified and in simplified form. But just how do we simplify these pure imaginary numbers?
- I quaranta giorni del Mussa Dagh (Italian Edition).
- DIOSES VII (Spanish Edition);
- Complex numbers;
- Intro to the imaginary numbers (video) | Khan Academy.
Let's take a closer look at the first example and see if we can think through the simplification. The following property explains the above "thought process" in mathematical terms. If we put this together with what we already know about simplifying radicals, we can simplify all pure imaginary numbers. Let's look at an example.
The work is shown below. I'd like to see another example. Let's practice some problems. Since there are no perfect square factors of 1 0 10 1 0 , this is as far as the simplification goes. Why do we have imaginary numbers anyway? The answer is simple.
Distance and midpoint of complex numbers. Distance of complex numbers Get 3 of 4 questions to level up! Midpoint of complex numbers Get 3 of 4 questions to level up!
Intro to the imaginary numbers
Multiplying complex numbers Opens a modal. Complex number operations review Opens a modal. Multiply complex numbers basic Get 3 of 4 questions to level up!
Multiply complex numbers Get 3 of 4 questions to level up! Complex conjugates and dividing complex numbers.
Latest Exhibits Related Plane-filling Curves. Well that's just going to be "i" to to the fourth times "i". We need the imaginary numbers for this! This is the same thing as, so this is "i" times negative "i", which is the same thing as negative one times, remember multiplication is commutative, if you're multiplying a bunch of numbers you can just switch the order. Skill Summary Legend Opens a modal.
Intro to complex number conjugates Opens a modal. Complex number conjugates Opens a modal. Dividing complex numbers Opens a modal.
- The Doctor, his Wife, and the Clock.
- The imaginary unit.
- St. Michaels Sword;
Dividing complex numbers review Opens a modal. Complex number conjugates Get 3 of 4 questions to level up!
Divide complex numbers Get 3 of 4 questions to level up! Absolute value and angle of complex numbers. Absolute value of complex numbers Opens a modal. Absolute value of complex numbers Get 3 of 4 questions to level up! Angle of complex numbers Get 3 of 4 questions to level up! Polar form of complex numbers. Complex number forms review Opens a modal. Multiplying and dividing complex numbers in polar form.
Visualizing complex number multiplication Opens a modal. Powers of complex numbers Opens a modal.