A complex number is represented as a+ib where a is real part and b is imaginary part. The complex number a+ib can also be represented as ordered pair(a,b) and plotted as a point in Argand plane. In this plane horizontal axis is called real axis and vertical axis is called imaginary axis.
An algebraic expression containing two terms is called binomial expression. The general form of the binomial expression is (x+a) and the expansion of (x+a)^n, where n is a natural number, is called binomial theorem. It gives a formula for the expansion of the powers of binomial expression.
The coefficients in the binomial expansion follow a specific pattern known as Pascal’s triangle.
Following are some important features of Pascal’s triangle.
-Each row is bounded by 1 on both sides.
-Any entry except first and last, is the sum of two entries in preceding row , one on the immediate left and other on immediate right.
Some important conclusions from the Binomial Theorem:
Total number of terms in binomial expansion is n+1.
The coefficients of terms equidistant from the beginning and end are equal. These coefficients are known as binomial coefficients.
The terms in the expansion of (x-a)^n are alternatively positive and negative first being positive always.
The coefficient of x^r in (r+1)th term in the expansion of (x+a)^n is (_r^n)C.
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The word equation is derived from word ‘equal’. Any expression having equal (=) sign is called equation. If any linear algebraic expression in one variable is equal to some integer or some other algebraic expression, then it is called algebraic equation.
Linear equations can be categorized as follows
1. When variable is only one side.
2. When variable is on both sides
When variable is only on one side: We always solve the equation for an unknown variable using the same operations on both sides so that equation doesn’t become uneven and both sides remain balanced.
When variable is on both sides:
When variables on both sides of equation, we try to bring the variables together either on left or on right side and then move forward with the same process of isolating variable
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