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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
Can a logarithmic function have a complex number?
Yes and as an example:
1. the natural log (ln) of 2+i3~1.28+.98i (base e or 2.71828)
2. The Log of 2+i3~.57+.43i (base 10)
What is a number of the form a plus bi where a is the real part and b is the imaginary part?
a complex number
Complex roots occur in conjugate pairs?
Not for all types of equations. But always in second degree equations they do.
Consider a third degree equation with 3 different roots. Obviously, one of the roots can not be in a pair.
How do you find all real and complex roots?
In general this question is unanswerable.
However, you can consider Newton's method to make very good estimates.
Equations can be very complex in that their curves have poles and zeros where you do not expect them. Consider Riemann's Zeta function Z(z) = Sum(1/n^z, n>0). It has complex zeros on the line z=1/2, but up to this date, the distribution of the zeros is not entirely known!
Yes. -10.39 is real because it does not have an imaginary component.
What is the worded form of 100000000000000000000000000000000000000000000000?
1 with 47 zeros. Ten to the forty seventh power.
Depending on what country you are in:
- one hundred quattuordecillion in the United States and some other English speaking countries.
- one hundred septilliard in many European countries.
See related link.
What set of numbers is the acute and which is the obtuse numbers on a protractor?
A right angle sits at 90o, which is right in the middle. Anything less than 90o, or to the left on the protractor are acute angles. Anything to the right, or bigger than 90o, would be considered an obtuse angle. A good way to remember this is that an acute angle is "a cute little angle."
In metamorphoses who transforms into a laurel?
Daphne, a patroness of Diana (Goddess of the Hunt), asked to be turned into a laurel tree after Apollo fell in love with her. She did not love him back and wished to remain an unmarried virgin, true only to Diana, for the rest of her life. Apollo pursued her and she finally begged the gods to be turned into the tree. Thus, to show his devotion, Apollo adopted the laurel tree as his sacred tree and wore the laurel leaves on his head as a crown.
How would you define the zero vector by using the idea of components?
All components of the zero vector equal to zero.
The complex roots of an equation are the complex numbers that are solutions to the equation.
How imaginary numbers are used in electricity into calculation?
'Complex numbers' are numbers that comprise 'real' and 'imaginary' numbers. In electrical engineering, we identify 'imaginary' numbers by placing a lower-case 'j' in front of them. For example, the complex number (10 + j5) comprises the 'real' number, 10, and an 'imaginary' number, 5.
We use complex numbers to locate points on a graph. Mathematicians call the horizontal axis of a graph the 'real axis', and they call the vertical axis the 'imaginary axis'. So 'imaginary' doesn't mean something that only exists in the mind, it's simply a mathematical term for the vertical axis of a graph. So the complex number (10 + j5) is used to represent a point which is located 10 units along the positive horizontal axis and 5 units along the positive vertical axis.
In alternating current theory, we use 'phasors' (a type of vector) to represent voltages or currents that lie at different angles to each other, so we can define them in terms of horizontal and vertical axes. In other words, every phasor can be defined in terms of real and imaginary numbers. We can then use the rules of 'complex mathematics' to multiply, divide, add, or subtract phasors -but that's another story!
Is 2 and a half a complex number number?
2 ½ is called a mixed number (a whole number and a fraction), not complex.
Complex number means there can be real and/or imaginary parts to a number. Without confusing you though, complex numbers include all of the real numbers (which include all fractions and mixed numbers).
The S transform in circuit analysis and design is method for transforming the differential equations describing a circuit in terms of dt into differential equations describing a circuit in terms of ds. With t representing the time domain and s representing the frequency domain.
Usually the writing of the time domain equations for the circuit is skipped and the circuit is redrawn in the frequency domain first and the equations are taken directly from this transformed circuit. This is actually much simpler and faster than transforming the time domain equations of the circuit would be.
The S transform and Laplace transform are related operations but different; the S transform operates on circuits and describes how they modify signals, the Laplace transform operates on signals.
a monomial itself is not a real number because it ia a vocabulary term, however, real numbers and vairables can be monmials.
What is the additive inverse of 9.1?
We are talking group theory here.
A group with addition has an additive inverse.
A group with multiplication has a multiplicative inverse.
The additive inverse of a number x is a y with x + y = 0.
The additive inverse of x is written -x.
Hence, the additive inverse of 9.1 equals -9.1.
The reason that this question can arise is that beyond groups, there are rings and fields. Rings and fields have, besides addition, also multiplication. An element can have an additive inverse and a multiplicative inverse at the same time.
