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Complex Numbers
The square root of negative one, which we now call the imaginary unit, was once thought to be an absurd notion. However, through the diligent studies of open-minded mathematicians, it was shown that the real numbers were actually just one part of a larger set of numbers known as the complex numbers, the other part being the imaginary numbers. Please direct all questions about these surprisingly useful and applicable numbers into this category.
887 Questions
Is an imaginary number always sometimes or never a complex number?
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.
How do you find complex zeros on a graph?
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.
Which is an example of an imaginary character based on a real person?
D. A fictional character who shares many qualities with the author's best friend
-Apex
What is the graphical relationship between a conjugate number and a complex number?
Graphically, the conjugate of a complex number is its reflection on the real axis.
Where did complex and imaginary numbers come from?
The 16th century Italian mathematician, Gerolamo Cardano was the first to use imaginary and complex numbers in his work on cubic equations.
How is an imaginary number defined?
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.
What complex number is a number of the form a plus bi where?
"a + bi" is a common way to write a complex number. Here, "a" and "b" are real numbers.Another common way to write a complex number is in polar coordinates - basically specifying the distance from zero, and an angle.
Square root of 17 in complex number terms?
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.
What is a number that can be written in the form a plus bi where a and b are real numbers?
A number of the form (a + bi) is a complex number.
How can I write (18 24i) as a complex number?
You can write it as (18, 24) or 18 + 24 i
Or use -24 if appropriate.
How can I write sqrt(18 plus 24i) as a complex number?
To take the square root of a complex number:* Write the original complex number in polar notation (absolute value and angle).
* For the square root, the angle will be half the angle. The absolute value will be the square root of that of the original number.
* There is a second square root: the same as above, but add 180 degrees (or pi, if using radians) to the angle.
* If you wish, you can convert the result(s) back to rectangular coordinates, i.e., real number + imaginary number.
Most scientific calculators have functions to convert from rectangular to polar and vice versa.
What is true about the complex number 5 - 5i?
Lots of things are true about that number. What specifically do you want to know?
Write ADT for complex numbers?
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).
Why is is not possible to find the polar representation of the complex number 0?
You can very well represent it as a polar number. But the angle is ambiguous; or rather, any angle will work.
Is one a real complex pure imaginary or nonreal complex number?
One is a complex number and a real number.
What are all of the real or complex numbers that are solutions to the equation x2-25?
x2 - 25 = 0 is x2 = 25 thus x = 5 or x = -5, only 2 real solutions
What is the product of these complex numbers (3-4i)(1-i)?
(3-4i)(1-i) = (3x1) + (3 x -i) + (-4i x 1) + ( -4i x -i) = 3 - 3i -4i -4 = -1 - 7i
What is the middle number of an ordered set of numbers?
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.
What strategy for finding the quotient when you divide a number by a power of 10 greater than 1?
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.
What is -9i 2-I as a complex 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 =
A non complex number is a number that does not have any imaginary component. An imaginary component is a non zero factor of the square root of -1, in other words, the imaginary number i.
