Complex Numbers

You can compare their magnitude (absolute values) but not the numbers themselves.

To graph (x^x), you first need to understand that the function is only defined for positive values of x. The real part of the graph will resemble a curve that starts at (0,1) and increases rapidly as x increases. The non-real part of the graph will involve complex numbers, which can be visualized in the complex plane as spirals around the origin, with the spirals getting closer together as x increases.

The reactance is taken imaginary because it does not consume any power directly but reactance like inductive or capacitive reactance provides phase shift of 90 degree, whether it provides a leading phase shift or lagging phase shift. In case of inductor the current lags voltage by 90 degree while in case of capacitor current leads by 90 degree. Thus only resistance is taken as real while combination of resistance and capacitance is called impedence....

Ashish Sharma AP ECE

HIET Shahpur

Complex numbers are basically "numbers in two dimensions". You can extend them to more dimensions; one superset that is sometimes used is the quaternions, which are numbers in four dimensions.

Always. The set of imaginary numbers is a subset of complex numbers. Think of complex numbers as a plane (2 dimensional). The real numbers exist on the horizontal axis. The pure imaginary are the vertical axis. All other points on the plane are combinations of real and imaginary. All points on the plane (including imaginary axis and real axis) are complex numbers.

A strategy for finding the quotient when you divide a number by a power of 10 greater than 1 by actually if you put them in decimals:

1/10=0.10

1/100=0.01

So the then 10 is bigger than 10.

1971

The Gee Whiz Story

So when Gilda Trozzolo, Pasquale's mother, decided to open a candy store, picking the name was easy. Gee Whiz Candy was established in 1971 in Elmwood Park, Illinois.

Lots of things are true about that number. What specifically do you want to know?

x2 - 25 = 0 is x2 = 25 thus x = 5 or x = -5, only 2 real solutions

(3-4i)(1-i) = (3x1) + (3 x -i) + (-4i x 1) + ( -4i x -i) = 3 - 3i -4i -4 = -1 - 7i

You can very well represent it as a polar number. But the angle is ambiguous; or rather, any angle will work.

If there is an odd number of elements in the set, then it is the median.

If there is an even number, then there is no middle number.

Basically you use a double-precision floating point number for the real part, a double-precision floating point number for the imaginary part, and write methods for any operation you want to include (such as addition, etc.; trigonometric functions, exponential function).

A positive real number, such as 17, has two square roots. One is the one your calculator gives you, if you use the square root function. The other is the same number, with a minus sign in front. None of these has an imaginary part. There are no additional complex roots that have a non-zero imaginary part.

A number of the form (a + bi) is a complex number.

It's actually quite hard to graph complex numbers - you would need a four-dimensional space to graph them adequately. I believe it's more convenient to find zeros analytically for such functions.

One is a complex number and a real number.

Unfortunately, due to the limitations of browsers, most mathematical symbols get removed and it leaves gibberish that is impossible to answer

Please edit/re submit your question with a full sentence of what you want solved, replacing mathematical symbols by words, eg plus for +, equals for =

An imaginary number is a continuous quantity that is the square root of a negative number and cannot be represented on the real number line.

The 16th century Italian mathematician, Gerolamo Cardano was the first to use imaginary and complex numbers in his work on cubic equations.

Graphically, the conjugate of a complex number is its reflection on the real axis.

I got -1.