Construction Of A Line SegmentTo draw a line segment of a given lengthWe can draw a line segment of a given length in two ways: (a) By using a scale (b) By using a pair of compassesConstruction: Draw a line segment of length 5.5 cm. (a) By using a scale…

Measure an Angle with a ProtractorMeasuring an AngleProtractor is a geometrical instrument that looks like the letter D. The angles are marked from 0° to 180° on the edge in clockwise direction as well as in anti-clockwise direction. O is the midpoint at…

Representing Complex Numbers Graphically (+ & -)Due to their unique nature, complex numbers cannot be represented on a normal set of coordinate axes.In 1806, J. R. Argand developed a method for displaying complex numbers graphically as a point in a …

Rational (Fractional) ExponentsRational (fractional) exponents are an alternate way to express roots Notice:   The denominator of the rational exponent becomes the index of the radical, and the numerator becomes the exponent of the radicand (expression …

Imaginary Unit and Standard Complex FormThe Imaginary Unit is defined as i =√-1The reason for the name “imaginary” numbers is that when these numbers were first proposed several hundred years ago, people could not “imagine” such a number. It is said that…

AC Method for Factoring TrinomialsConsider this unconventional method of factoring trinomials: Why it works:The secret to understanding this method is to realize that these steps are actually a shorthand for a more complex process of multiplication and r…

What is a Linear EquationLet us consider a small puzzle: Think of a number and add 7 to get 12. What is the number? We can easily say that the number must be 5. If we use a letter, i.e., (variable) to stand for the unknown number, we can write this puzz…

Cyclic Nature of the Powers of iTo be cyclic means to be repetitive in nature. When the imaginary unit, i, is raised to increasingly larger powers, it creates a cyclic pattern.The powers of i repeat in a definite pattern: ( i, -1, -i, 1 ) When raising…

Open and Closed Figures in GeometryClosed Figures: Figures in which initial and end points coincide with each other are called closed figures. Examples: Open Figures: Figures which have different initial and end points are called open figures. Examples: …

Comparison of Line SegmentsComparing two line segments means finding the shorter or longer line segment. The methods that compare the length of line segments are as follows:Comparison by observationFigure shows two line segments AB and CD. Just by observ…