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The answer is relatively simple if you know hyperbolic functions.
Suppose x is real so that ix is an imaginary number.
Then tanh x = -i*tan(ix)
So tan(ix) = (tanh x )/-i = i*tanh x
= i * sinh x/csh x = i*(ex - e-x)/(ex + e-x) = i*(1 - e-2x)/(1 + e-2x)
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∙ 10y ago
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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.
Can you divide an imaginary number by a real number?
an imaginary number is imaginary so no (i guess) this answer kind of sucks
How do you simplify the imaginary number -125?
-125 is NOT an imaginary number.
Why do you say that pi is an imaginary number?
If I ask Answers™ "what is pi squared?" I find "It is approximately equal to 3.14 but in reality pi is an imaginary number that has no end." The answer also goes on to tell me that imaginary numbers cannot be multiplied by themselves. Now i must see what y'all have to say about imaginary numbers...
Whats an imaginary number?
An imaginary number is a number that has the square root of -1 as one of its factors.
What is the mathematical importance of imaginary numbers?
The mathematical importance of an imaginary number is to allow the result of a square root of the imaginary number to equal a negative number. One can find more extensive information on imaginary numbers and their importance on the Wikipedia website.
How do you find the slope of an Indifference curve?
You find the tangent to the curve at the point of interest and then find the slope of the tangent.
How do you find x assume that segments that appear tangent are tangent?
A tangent refers to the way in which a curve is measured. The amount of deviation from the segment line is measures, then a formula applied to find the tangent.
Can a number be imaginary but not pure imaginary?
Yes. The number 1 + i is imaginary but not pure imaginary, while 5i is pure imaginary.
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.
Find the Square Root -81?
There is no square root for a negative number. It is an imaginary number.
Can you divide an imaginary number by a real number?
an imaginary number is imaginary so no (i guess) this answer kind of sucks
How do you convert j equations to phase angle equation?
The phase angle is the angle that has a tangent of (imaginary part)/(real part).
How do you simplify the imaginary number -125?
-125 is NOT an imaginary number.
What does 7 divided by imaginary number equal?
That quotient would be an imaginary number. The actual number depends on exactly what imaginary number you divide the 7 by.
Why do you say that pi is an imaginary number?
If I ask Answers™ "what is pi squared?" I find "It is approximately equal to 3.14 but in reality pi is an imaginary number that has no end." The answer also goes on to tell me that imaginary numbers cannot be multiplied by themselves. Now i must see what y'all have to say about imaginary numbers...
Is the difference of a complex number and its conjugate a real imaginary or pure imaginary number?
It is a pure imaginary number.Since (a+bi)-(a-bi) = 2bi, it is a pure imaginary number (it has no real component).
