A complex number is a number of the form a + bi, where ‘a’ and ‘b’ are real numbers and ‘I’ is an indeterminate satisfying i2 = −1. For example, 2 + 3i is a complex number. The equations x2 + 5 = 0, x2 + 10 = 0, x2 = -1 are not solvable […]
.....Science
Multiplication of Two Complex Numbers
A complex number is a number of the form a + bi, where ‘a’ and ‘b’ are real numbers and ‘I’ is an indeterminate satisfying i2 = −1. For example, 2 + 3i is a complex number. The equations x2 + 5 = 0, x2 + 10 = 0, x2 = -1 are not solvable in the real number […]
.....Subtraction of Complex Numbers
Subtraction of Complex Numbers A complex number is a number of the form a + bi, where ‘a’ and ‘b’ are real numbers and ‘I’ is an indeterminate satisfying i2 = −1. For example, 2 + 3i is a complex number. The equations x2 + 5 = 0, x2 + 10 = 0, x2 = […]
.....Equality of Complex Numbers
Equality of Complex Numbers A Complex Number is a combination of a Real Number and an Imaginary Number. A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and ‘i’ is a solution of the equation x2 = −1, which is called […]
.....Comparison of Surds
Definitions of surds: A root of a positive real quantity is called a surd if its value cannot be exactly determined. It is a number that can’t be simplified to remove a square root (or cube root etc). For example, each of the quantities √3, ∛7, ∜19, (16)^2/5 etc. is a surd. More Examples.....
Direct Variation in Mathematics
“Variation” defines a concept that deals with variability in mathematics. Variation is defined by any change in some quantity due to change in another. We often come across with different types of variation problems in mathematics. Variation problems involve fairly simple relationships or for.....
Classification of Triangles on the Basis of their Angles
Triangle is a plane figure with three straight sides and three angles. The three angles always add to 180°. The vertex is a corner of the triangle. Every triangle has three vertices. The interior angles of a triangle always add up to 180°. The exterior angles of a triangle always add up to 360.....
Classification of Triangles on the Basis of their Sides
Triangle is a plane figure with three straight sides and three angles. The three angles always add to 180°. The vertex is a corner of the triangle. Every triangle has three vertices. The interior angles of a triangle always add up to 180°. The exterior angles of a triangle always add up to 360.....
Medians of a Triangle
Medians of a Triangle A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Triangle is a plane figure with three straight sides and three angles. The three angles always add to 180°. The vertex is a corner of the triangle. Every triangle has three verti.....
Geometrical Property of Altitudes
Geometrical Property of Altitudes Sometimes the opposite side isn’t quite long enough to draw an altitude, so we are allowed to extend it to make an altitude possible. This line containing the opposite side is called the extended base of the altitude. The intersection of the extended base and t.....
Altitude of a Triangle
Altitude of a Triangle In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base. The definition of the altitude of a triangle is a line that extends from one vertex of a triangle perpendicular to the opposite side. Sometimes the opp.....
Properties of Angles of a Triangle
Triangle is a plane figure with three straight sides and three angles. The three angles always add to 180°. The vertex is a corner of the triangle. Every triangle has three vertices. The interior angles of a triangle always add up to 180°. The exterior angles of a triangle always add up to 360.....