Negative of a Complex number
If Z = a + ib, then Z is called the negative of Z. -Z = -(a + ib) = -a - ..
Irrational Numbers
Numbers which are not rational are called irrational numbers. When expressed as decimals, they are non-terminating and non-recurring. We can obtain infinite number of irrationals between two irrational numbers..
Complex number
Square root of a negative number is known as an imaginary number . If x and y are real numbers, then x + iy is called a complex number . x is called the real part and y is called the imaginary part . The fo..
Questions on Number theory
Question 1 - Question: Define an even number. Answer: A number which is divisible by 2 is called an even number..
Polar form of a Complex number
z = r{cos q +isin q } is called the polar form of the complex number. x + iy (which is in the cartesian form) where is called the modulus of the complex number z denoted by |z| and q = tan -1 y/x is called the amplitude or argument..
z = r{cos q +isin q } is called the polar form of the complex number. x + iy (which is in the cartesian form) where is called the modulus of the complex number z denoted by |z| and q = tan -1 y/x is called the amplitude or argument..Compounded ratio
If two or more ratios are multiplied term-wise, the ratio thus formed is called their compounded rati..
Definition of ratio
If a and b are two quantities with the same units such that b is not equal to zero; then the quotient a/b is called the ratio between a and b. It is written as a:b. Ratio does not have any unit. The quantities a and b are called terms of the ratio. a' is called a..
Singleton Set or Singlets
A set consisting of a single element is called a singleton set or singlet. The cardinality of the singleton set is ..
Exponential form of a Complex number
If z = x + iy then e z = e (x + iy) = e x e iy ? e z = e x {cos y + i sin y} is called the Exponential form of the Complex number..
Ratio and Proportion I
Ratio: If a and b are two quantities with the same units such that b is not equal to zero; then the quotient a/b is called the ratio between a and b. It is written as a:b. Ratio does not have any unit. The quantities a and b are called terms of the ratio. a' is calle..
Result
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