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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
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.
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).
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 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.
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 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.
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.
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 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.
Is one a real complex pure imaginary or nonreal complex number?
One is a complex number and a real number.
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 true about the complex number 5 - 5i?
Lots of things are true about that number. What specifically do you want to know?
Can a no real number be a pure imaginary number?
If a number is pure imaginary then it has no real component. If it is a real number, then there is no imaginary component. If it has both real and imaginary components, then it is a complex number.
Who first used the term imaginary to describe numbers?
It looks like it was most likely Rafael Bombelli in 1572, from what I can find. I've posted a related link to a Wikipedia article. Wikipedia should not be your sole source of information, but it's a starting point.
To get the complex conjugate, change the sign in front of the imaginary part. Thus, the complex conjugate of -4 + 5i is -4 - 5i.
Find the complex conjugate of 14 plus 12i?
To find the complex conjugate of a number, change the sign in front of the imaginary part. Thus, the complex conjugate of 14 + 12i is simply 14 - 12i.
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.
Find the absolute value of the complex number z equals 3 plus 4i?
('|x|' = Absolute value of x)
|3+4i| = √(32 + 42)
= √(9+16)
= √25
= 5
Thus |3+4i| = 5.
Not exactly. The numbers (a & b) can be any real number (positive or negative). It is the letter i, which represents the imaginary unit sqrt(-1).
False
How do you subtract imaginary numbers?
When adding and subtracting complex numbers, you can treat the "i" as any variable. For example, 5i + 3i = 8i, 5i -3i = 2i, etc.; (2 + 5i) - (3 - 3i) = (2 - 3) + (5 + 3)i = -1 + 8i.
