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Quadratic Equations - Coggle Diagram
Quadratic Equations
Definiton
ax² + bx + c = 0
solutions of quadratic equation
completing the square
Completing the square is a method that is used for converting a quadratic expression of the form ax2 + bx + c to the vertex form a(x - h)2 + k. The most common application of completing the square is in solving a quadratic equation.
Factoring
if we can factorise ax2 + bx + c ≠0, into a product of two linear factors, then the roots of the quadratic equation ax2 + bx + c = 0 can be found by equating each factor to zero
quadratic formula
The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) . See examples of using the formula to solve a variety of equations..
Complex numbers
Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and ‘i’ is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).
The complex number is basically the combination of a real number and an imaginary number. The complex number is in the form of a+ib, where a = real number and ib = imaginary number. Also, a,b belongs to real numbers and i = √-1.
Hence, a complex number is a simple representation of addition of two numbers, i.e., real number and an imaginary number. One part of it is purely real and the other part is purely imaginary.
What are Imaginary Numbers
Definiton and formulas
The numbers which are not real are imaginary numbers. When we square an imaginary number, it gives a negative result. It is represented as Im(). Example: √-2, √-7, √-11 are all imaginary numbers.
The complex numbers were introduced to solve the equation x2+1 = 0. The roots of the equation are of form x = ±√-1 and no real roots exist. Thus, with the introduction of complex numbers, we have Imaginary roots.
We denote √-1 with the symbol ‘i’, which denotes Iota (Imaginary number).
What are Real numbers
Any number which is present in a number system such as positive, negative, zero, integer, rational, irrational, fractions, etc. are real numbers. It is represented as Re(). For example: 12, -45, 0, 1/7, 2.8, √5, etc., are all real numbers.
Imaginary unit
i1 = i
i2 = −1
i0 = 1
i3 = −i
i4 = 1
conjugate of a complex number
A complex conjugate is formed by changing the sign between two terms in a complex number. Let's look at an example: 4 - 7i and 4 + 7i. These complex numbers are a pair of complex conjugates. The real part (the number 4) in each complex number is the same, but the imaginary parts (7i) have opposite signs
