0
If z equals a plus ib then show that arg conjugate of z equals 2pi -arg z?
Lipikasingh
If z = a + ib
then
arg(z) = arctan(b/a)
Let z' denote the conjugate of z. Therefore, z' = a - ib
Then
arg(z') = arctan(-b/a) = 2*pi - arctan(b/a) = 2*pi - arg(z)
Wiki User
∙ 9y ago
Add your answer:
Earn +20 pts
2pi is an integer?
2 times pi is not an integer. Since Pi is an irrational number, 2 pi is also an irrational number.
Will the sum of two irrational numbers always be rational?
Consider pi and 4 - pi. 4 - pi + pi = 4, which is clearly rational. However, both pi and 4 - pi are irrational, as you can verify. plz to be lerning numburs Then consider pi + pi = 2pi, which is clearly irrational. The sum of two irrational numbers, therefore, may or may not be rational.
Find the square root of a complex number system?
Probably the best way is to change the complex number to its polar form, [or the A*eiΘ form] A is the magnitude or the distance from the origin to the point iin the complex plane, and Θ is the angle (in radians) measured counterclockwise from the positive real axis to the point. To find the square root of a number in this form, take the positive square root of the magnitude, then divide the angle by 2. Since there will always be 2 square roots for every number, to find the second root, add 2pi radians to the original angle, then divide by 2. Take an easy example of square root of 4. Which we know is 2 and -2. OK so the magnitude is 4 and the angle is 0 radians. zero divided by 2 is zero, and the positive square root of 4 is 2. Now for the other square root. Add 2pi radians to 0, which is 2pi, then divide by 2, which is pi. pi radians [same as 180°] points in the negative real direction (on the horizontal), so we have ei*pi = -1 and then multiply by sqrt(4) = -2. Try square root of i. i points straight up (pi/2 radians) with magnitude of 1. So the magnitude of the square root is still 1, but it points at pi/4 radians (45°). Converting back to rectangular gives you sqrt(2)/2 + i*sqrt(2)/2. The other square root will always point in the opposite direction [180° or pi radians]. So the other square root is at 225° or 5pi/4 radians, and the rectangular for this is -sqrt(2)/2 - i*sqrt(2)/2. Using FOIL (from Algebra) you can multiply it out like two binomials and you will get i when you square either of the two answers for square root.
Is the sum of 2 irrational numbers rational?
No. The irrational parts may cancel out.For example, 1 + sqrt(2) and 5 - sqrt(2) are both irrational but their sum is 1 + 5 = 6.
What is the POLAR form of complex numbers?
By creating a real-imaginary plane (real on horizontal axis, imaginary on vertical), any complex number can be represented graphically. The polar form is a magnitude and angle. The magnitude is measured from the origin to the point on the plane. For a complex number a + bi, this value is a2 + b2. The angle is measured from the positive real axis, clockwise. For positive imaginary part (b), this will be +arccos(a/(a2 + b2)). (0° to +180°, or 0 to +pi radians) For negative imaginary part (b), this will be -arccos(a/(a2 + b2)). (0° to -180°, or 0 to -pi radians, or alternatively 180° to 360° or pi to 2pi radians)
Pie plus pie equals what?
If you mean the number pi, pi + pi is usually written as 2pi.
Determine the period of y equals -3 sin x?
the period is 2pi. period is 2pi/b and the formula is y=AsinBx.
What is the phase shift for sin 2pi plus pi?
Assuming you mean that the pi is not within the sin(2pi), its a vertical shift of +pi
Formula of r form c equals 2pi r?
The circumference of a circle C is 2Pixr So solving for r we have C/2Pi=r
What equation is this x equals a sin wt?
sine wave, with a period of 2pi/w
What is the reciprocal of 2pi?
Reciprocal of 2pi = 1/(2pi) = 0.159155(rounded)
What is the radius fomula?
r = c/2pi (radius of a circle equals the circumference divided by (2 x pi)
What is the period of the graph of y equals 2 sin 3x plot?
Two thirds pi, or rather 2pi/3.
What is the period of y equals sin x?
The period is the length of x over which the equation repeats itself. In this case, y=sin x delivers y=0 at x=0 at a gradient of 1. y next equals 0 when x equals pi, but at this point the gradient is minus 1. y next equals 0 when x equals 2pi, and at this point the gradient is 1 again. Therefore the period of y=sinx is 2pi.
What is pi plus pi?
pi+pi is 6.28. all that you have to do is add up the numbers.-fromama fromamzez.webs.com
What is cos 2pi?
The cos of 2pi is 360 degrees which is 1.
What is pi added to pi over two?
(pi^2+2pi)/2pi
