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Harmonic Progression (H.P.)
A sequence of numbers is said to form a harmonic progression if their reciprocals form an arithmetic progressio..
Harmonic Mean (H.M.)
If three quantities are in harmonic progression, then the middle quantity is called the harmonic mean between the other two. Example: 1/3, 1/7, 1/11 are in H.P., then 1/7 is the middle term. Hence 1/7 is the harmonic mean between 1/3 and 1/1..
Harmonic Mean (H.M.)
If three quantities are in harmonic progression, then the middle quantity is called the harmonic mean between the other tw..
To insert n Harmonic Means between two given quantities
Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and ..
Note 4:
The last term in L.H.S of (ii) and (iii)will depend on the fact as to whether n is even or od..
To find the qth roots of a Complex number
One of the most important applications of De Moivre's theorem is to find the q t h roots of a complex number. Let z = x + iy be a complex number. Let z = r {cos q + i sin q } be its polar form. And z 1/q be the q th root of z. Through De ..
number of neutrons in h
Question and Answers 2 Question and Answers 2.1 Question and Answers 2.2 Question and Answers 2.3 Question and Answers 2.4 ..
qth root complex number Argand diagram
Argand diagram of the q th roots of a Complex number - All the q-th roots of z lie on a circle centred at the origin O and having radius equal to the real, positive q t h root of r. One of them has amplitude and others are uniformly spaced around the circle separated from others..
Note 1:
The L.H.S of (ii) and (iii) will have only finite number of terms, because n C r = 0 in case r>..
Minors
Let |aij| be a determinant of order n. The determinant obtained by deleting the i t h row and j t h column in which the element a i j lies is called the minor of element a i j and is denoted by M i ..
Result
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