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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 do you write 240 million in standard form?
To write 240 million in standard form, you would express it as 2.4 x 10^8. This is because the number 240 million can be broken down into 2.4 multiplied by 100 million (10^8). Standard form is a way of writing large numbers using powers of 10 to represent the value.
Is chanel number 10218484 real?
Most likely no. TV channels will probably only hold 2 to 3 dights. I haven't seen a TV with 4+ dights.
What is a specific number set as a goal?
A specific number set as a goal is typically referred to as a target or a benchmark. In various contexts, such as in education, business, or sports, setting a specific numerical goal helps individuals or organizations track progress and measure success. These goals are often SMART (Specific, Measurable, Achievable, Relevant, Time-bound) to ensure they are clear and attainable.
What are the six steps of complex division?
1. Divide
2. Multiply (compare)
3. Subtract
4. Compare
5. Bring down
6. Start over
Similar factions are fraction that have the same denominator ^^
How are complex numbers and real numbers related?
Complex numbers extend the concept of real numbers by introducing an imaginary unit, denoted as "i." Real numbers can be considered a subset of complex numbers with the imaginary part equal to zero. Complex numbers include both a real and imaginary component, allowing for operations like addition, subtraction, multiplication, and division.
What is the first step when dividing complex numbers?
You multiply both the numerator and denominator my the complex conjugate of the denominator. For example if you have. a+bi/c+di you would multiply both the top and bottom by c-di. This is in effect multiplying by 1.
Mapping of complex numbers in complex plane?
In the complex plane, each complex number is represented by a point, with the real part as the x-coordinate and the imaginary part as the y-coordinate. The mapping of complex numbers in the complex plane allows us to visualize operations like addition, subtraction, multiplication, and division geometrically. It also enables us to study properties such as modulus, argument, and conjugate of complex numbers.
How zeros are in a bicentillion?
A: "bicentillion" doesn't exist, I think you mean: centillion, or here in Britan a vigintillion, a vigintillion has 120 zeros after it and a centillion has 303 zeros after it.
Gang-nam is a city in south Korea where Psy was raised it translates into English as city south of river it is a business city but Psy claims the style there is dress classy act cheesy
so when Psy says Gang-nam style he means in the style of the people of Gang-nam
What are the applications of complex numbers in civil engineering and building?
This is a rather loose application. The related link shows the fluid flow field of two
water sources near each other.
Refer to related link down below.
How to calculate sum of two complex number in c plus plus?
typedef struct complex {
double real, imag;
} complex;
...
complex x, y, z;
...
/* add */
z.real = x.real + y.real;
z.imag = x.imag + y.imag;
/* sub */
z.real = x.real - y.real;
z.imag = x.imag - y.imag;
/* mul */
z.real = x.real*y.real - x.imag*y.imag;
z.imag =x.imag*y.real + x.real*y.imag;
/* div */
double d = y.real*y.real + y.imag*y.imag;
z.real = (x.real*y.real + x.imag*y.imag)/d;
z.imag = (x.imag*y.real - x.real*y.imag)/d;
The conjugate of a complex number can be found by multiplying the imaginary part by -1, then adding the "real" part back. (-2i) * -1 = 2i, so the conjugation is 7+2i
How do you solve complex fraction?
this is a very good question. lets solve (2+3i)/(4-2i).
we want to make 4-2i real by multiplying it by the conjugate, or 4+2i
(4-2i)(4+2i)=16-8i+8i+4=20, now we have
(2+3i)/20 0r 1/10 + 3i/20
notice that -2i times 2i = -4i^2 =-4 times -1 = 4
What is the domain of the variable x if it's an imaginary number?
In (x+iy), x=any value in the real number line.
What are some unique properties of imaginary numbers?
1. i1 = i, i2= -1, i3= -i, i4= 1, i5= i, i6= -1 and so on.
2. Euler's constant e, when raised to the power of a complex number, gives a point in the complex plane according to Euler's Identity, e^(iθ
) = cos(θ
) + i*sin(θ
).
Whenθ
is replacedby pi, we get:
e^(iπ)
= cos(π
) + i*sin(π
)
= -1 + 0
= -1
In other words, e^(iπ)
+ 1 = 0.
3. Many intriguing fractals have been discovered in the complex plane, the most famous of which is the Mandelbrot Set. This is formed by an iterative process of a point in the plane. It produces a beautiful image, nicknamed by many as the "Thumbprint of God". (Google Images is your friend here - check it out.)
4. De Moivre's Theorem holds true in the realm of the imaginary, stating that
(r cisθ
)n= rncis nθ
.
This is a fascinating theorm in itself, but it also has hidden implications.
For example, if r = 1 (the point was 1 unit away from the origin), and you were to plot this point with a small angle above the positive real axis, then raising this number to an increasing power would result in that point making a full revolution about the origin and coming right back to where it started.
This is because rnstays the same (1^(anything) = 1), but the angle is slowly increasing as the power does. Therefore, as the angle increases, a circle is plotted around the origin with radius 1.
There are many other fascinations around complex numbers, but this covers the basics.
