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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
How much is one score in terms of mathematic number and time?
A score in time eans 20 years "four score and seven years ago" means 87
What is the correct notation for writing complex numbers?
a + ib
where a is the real part, and b is the imaginary part.
Write a c Program to add subtract multiply and divide the two complex numbers?
#include<stdio.h>
#include<conio.h>
void main()
{
int a,b,c,d,e,ch;
clrscr();
printf("enter 1st no\n");
scanf("%d",&a);
printf("2nd no\n");
scanf("%d",&b);
priintf("enter choice 1.add 2.sub 3.mul\n");
scanf("%d",&ch);
switch(ch)
case 1:
c=a+b;
printf("%d",c);
break;
case 2:
d=a-b;
printf("%d",d);
break;
case 3:
e=a*b;
printf("%d",e);
break;
}
getch();
}
The square root of 2 is
1.4142135623730950488016887242096980785696718753769480731766797379907324784621
Ans. 2 The square root of 2 is irrational; that means that it can not be expressed by a fraction,. Any decimal that terminates or repeats is a fraction; this means that an attempt to express root 2 by a decimal can never be exact.
For most everyday purposes people use 1.414 when they need an approximation. The decimal given above is a much closer approximation, but still not exact.
Note. The qn says what is sqrt-2 ?. Both answerers have assumed that the questioner meant sqrt(2), or 21/2.
If the qn really was "what is ( -2) 1/2 ", everything above should be multiplied by i. i is the square root of -1, a so-called imaginary number.
How many complex number solutions can exist for a quadratic equation?
Quadratic equations always have 2 solutions. The solutions may be 2 real numbers (think of a parabola crossing the x axis at 2 different points) or it could have a "double root" real solution (think of a parabola just touching the x-axis at its vertex), or it can have complex roots (which will be complex conjugates of each other). For the last scenario, the graph of the parabola will not touch the x axis.
How long would it take to pay off a debt of 80 trillion dollars?
That would depend on several variables:
-- The interest rate on the debt.
-- How often you make a payment.
-- The amount of each payment.
What is complex number operation?
You can do all of the operations with complex numbers that you can do with real numbers but they can be more complicated. Finding the 1/3 root of 8 is easy but how
about finding (2-3.7i)^1/3 is more difficult. Also graphing something like w=(z-1)/(z+1) makes interesting images.
Please see the Related Link below.
A terabyte is one trillion bytes (1012 = 1,000,000,000,000 bytes) in current standard usage.
1 terabyte (TB) = 1,000 gigabytes (GB) = 1,000,000 megabytes (MB)
(There is a similar unit, the terabinary byte, or "tebibyte", which is 240 or 10244 = 1,099,511,627,776 bytes. However, this unit is never actually used, as hard drives are the only things that can hold this much, and they are always measured in powers of 10.)
How do you create a class of complex numbers?
I assume you refer to programming. Classes of complex numbers already exist for many programming languages (for instance, for Java); if you search for them, you can just use the ready-made classes, or - if you have a classroom task of writing your own class - at least get some useful ideas.The general idea is that you define a class with two fields - in Java that would be fields of type "double" - to store the real and imaginary part. Then you define methods for the desired operation and functions, such as addition, subtraction, multiplication, division, sine, cosine, exp, etc.
As an example, to add two numbers, the method "add" can add the number in the object on which it is invoked, and the other number can be passed as a parameter (argument); the answer can be written back to the object. This would be equivalent to:
a = a + b
As an alternative, you can pass two parameters (other complex numbers - i.e., other objects of the type "complex"), and make your object equal to the sum of the two. This would be equivalent to:
a = b + c
How do you pronounce or read a complex number?
Complex numbers include a multiple of the imaginary number constant "i" which is the square root of -1. The constant "2i " can be pronounced as "two-eye" or "two imaginary". (where confusion is possible with the electrical current "i", the letter "j" is often used.
What is the meaning of complex?
The state of being complex; intricacy; entanglement., That which is complex; intricacy; complication.
Is 616 the real number of the beast?
"Let he who has understanding reckon the number of the beast, for it is a human number, its number is six hundred and sixty-six."
666 is the original number of the beast, but 616 has been seen to pop up in other holy books.
"conjugate"
That step is called "rationalizing the denominator", although it actually makes
the denominator 'real', but not necessarily 'rational'.
How to calculate the division of complex number?
for two numbers: a + bi and c + di in rectangular format: (a + bi)/(c + di) can be calculated as follows:
Multiply numerator and denominator by complex conjugate of the denominator: ( c - di).
This gives (ac - bd + bci - bdi) / (c2 + d2). Now the denominator is a real number.
If you have them in polar form: Magnitude<Angle. Then divide the magnitudes and subtract the angles.
What is the meaning of powers and roots in complex numbers?
The meanings are the same but getting the answers use different rules. Ex:
1. None complex-(x+y)^2=xx+yy+2xy and is a family of parallel lines.
2. Complex-(x+iy)^2 Now notice the "i operator" and how it is used in the computation. (x+iy)(x+iy)=xx+i2xy+iiyy. Now i=(-1)^.5, so ii=-1 and so we have
xx-yy+i2xy. If we graph this out, we get families of parabolas at right angles to
each other. The (xx-yy) are the real and at right angles to the i2xy, the imaginaries.
Maybe somebody else can tackle the roots.
Is the sum of two conjugate complex number a real number?
Not necessarily. It can be wholly imaginary.
For example, 1 + i actually has two complex conjugates. Most schools will teach you that the complex conjugate is 1 - i. However, -1 + i is also a conjugate for 1 + i. (Their product is -1 times the product of the "normal" conjugate pair).
The sum of 1 + i and -1 + i = 2i
Yes - 67 is real because it does not have an imaginary component.
What are important in complex numbers CHAPTER?
I don't exactly know what you're looking for in an answer. I'll direct you to the Answers.com video on Complex Numbers. See Related Link.
How do you write in numerals nine hundred ninety nine and nine thousand?
Nine hundred and ninety-nine is 999
Nine thousand is 9,000
Why complex numbers can not b compared?
I would say that complex numbers can be compared almost as easily as natural numbers.
Complex numbers consist of a real part and an imaginary part.
Often written a+bi - i being the imaginary unit.
If 'b' in the above equation is zero, then bi = 0.Then we don't have a imaginary part and the number is real.
If 8 is greater than 5, then we could say that 8+8i is greater than 5+5i for both the real and the imaginary part.
What are the 5 example of real number?
Basically 1, 2, 3, 4, 5 are all real numbers, but as a real number doesn't only limit of integers, it can be 2/5, √2, or even π.
How to add and subtract complex numbers?
Handle the real parts and the imaginary parts separately.
Don't try to borrow ("regroup") or carry. It can't be done.
To find the real part of the sum, add the real parts.
To find the real part of the difference, subtract the real parts.
To find the imaginary part of the sum, add the imaginary parts.
To find the imaginary part of the difference, subtract the imaginary parts.
ExampleSuppose you want to add the following complex numbers: 3-2i and -7-6i.The real part is 3-7, which is -4.
The imaginary part is -2i+(-6i), which is -8i (because -2+(-6)=-8).
So the answer is -4-8i.
It's just like adding expressionsYou've probably done things like (4-7x) + (-6+x). In that case, just pretend i is x when you're doing these problems. (It works for multiplying too, except that when you get an i2 term you should substitute i2 = -1 )