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Multiply and Divide Complex Numbers 150 150 SchoolTutoring Academy

Multiply and Divide Complex Numbers

Multiplication of Complex Numbers The product of complex numbers a + bi and c + di is given as: (a + bi) + (c + di) = (ac – bd) + (ad + bc)i Example: (4 – 2i)(3 + 5i) = 4(3 + 5i) – 2i(3 + 5i)                           (Using distributive property over addition) = 12…

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Conjugate, Addition and Subtraction of Complex Numbers 150 150 SchoolTutoring Academy

Conjugate, Addition and Subtraction of Complex Numbers

Conjugate of complex number The conjugate of a complex number z = a + bi is: a – bi Example: Conjugate of 7 – 5i = 7 + 5i Addition of Complex Numbers Sum of two complex numbers a + bi and c + di is given as: (a + bi) + (c + di)…

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Algebraic Identities 150 150 SchoolTutoring Academy

Algebraic Identities

Solving algebraic problems get easy with readily available expressions. These expressions are knows as algebraic identities or rules which makes the job of a person easy, fast and reduces the chances of error. Below are most commonly used algebraic identities: Square of a Binomial (a + b)2 = a2 + 2ab + b2 Example: (x…

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Imaginary Numbers: Understanding the Imaginary Part 150 150 SchoolTutoring Academy

Imaginary Numbers: Understanding the Imaginary Part

We are told that we cannot take square root of a negative number. However, we can take the square root of a negative number, but it involves using a new number to do it. This new number was called ‘i’ stands for imaginary. The imaginary is defined as:              …

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Introduction to Complex Numbers 150 150 SchoolTutoring Academy

Introduction to Complex Numbers

A complex number is a number which can be put in the form a + bi, where a and b are real numbers and i is called the imaginary unit, where i2 = −1, a is called the real part and b the imaginary part of the complex number. Representation of a complex number A…

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Scientific Notation 150 150 SchoolTutoring Academy

Scientific Notation

Scientific notation is a way of writing numbers that are too large or too small to be conveniently written in standard notation. In scientific notation the number is written as: R × 10b where, the coefficient R is a real number called significand and exponent b is an integer. The exponent shows the number of…

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Triangle Inequality Theorem 150 150 SchoolTutoring Academy

Triangle Inequality Theorem

The Triangle Inequality theorem states that: “The sum of the lengths of any two sides of a triangle is greater than the length of the third side.” Otherwise, a triangle cannot be created. Below is triangle ABC, with sides AB, BC and AC.   According to triangle inequality theorem, AB + BC > AC AC…

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Acids and Bases 150 150 SchoolTutoring Academy

Acids and Bases

By the definition of Svante Arrhenius, an acid is a material that can release a proton or hydrogen ion (H+). Hydrogen chloride in water solution ionizes and becomes hydrogen ions and chloride ions. HCl –> H+ + Cl– A base, or alkali, is a material that can donate a hydroxide ion (OH–). Sodium hydroxide in…

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Inverse Relationship Between Logarithmic and Exponential Functions 150 150 SchoolTutoring Academy

Inverse Relationship Between Logarithmic and Exponential Functions

There is inverse relationship between logarithmic and exponential functions given by expressions below: If, y = ax then, x = loga(y) That is, if x raise to power a is y, then log to base a of y is x. Example 1: If 1000 = 103 then, log10(1000) = 3 Example 2: If 9 =…

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SchoolTutoring Academy – General Chemistry Review of Mixtures 150 150 SchoolTutoring Academy

SchoolTutoring Academy – General Chemistry Review of Mixtures

A mixture is a combination of two or more substances that do not chemically combined and do not exist in fixed proportions to each other. Mixture refers to the physical combination of two or more substances the identities of which are retained. There is no chemical change to the constituents of a mixture but the…

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