Example for complex conjugates

In grade 10 math , complex conjugates are a pair of complex numbers, both having the same real part, but with imaginary parts of opposite signs. For example, 3 + 4i and 3 - 4i are complex conjugates.
The conjugate of the complex number z

where a and b are real numbers, is

An alternate notation for the complex conjugate is z * . However, the notation avoids confusion with the notation for the conjugate transpose of a matrix, which can be thought of as a generalization of complex conjugation. If a complex number is represented as a 2×2 matrix, the notations are identical.We also can use scientific notation converter to find the number.

Let's an example problem from numeric and algebraic operations


Question:-

How do you use complex conjugates to find (3+7i)/(2-i) ?


Answer:-


In the Given problem the denominator is (2-i)

So ,it's conjugate is (2+i)

Multiplying both numerator and denominator with (2+i)

= (3+7i)(2+i)/(2-i)(2+i)

= (5+17i)/(4-i²)

We know that i² = -1

= (5+17i)/4+1

= (5+17i)/5 Answer

Problem on Order of Operations

In mathematics and computer programming, an expression or string of symbols is intended to represent a numerical value; a properly-formed expression may be evaluated in an unambiguous way. But in practice, an expression with multiple terms and operators may be written without parentheses, in which case the intended value of the expression is determined by convention. When a term in the expression is both preceded and followed by an operator such as minus or times, a convention is needed to clarify which operator should be applied first; this rule is known as a precedence rule, or more informally order of operation. From the earliest use of mathematical notation[citation needed], multiplication took precedence over addition, whichever side of a number it appeared on. Thus 3 + 4 × 5 = 5 × 4 + 3 = 23. When numeric and algebraic operations were first introduced, in the 16th and 17th centuries, exponents took precedence over both addition and multiplication, and could be placed only as a superscript to the right of their base. Thus 3 + 5 2 = 28 and 3 × 5 2 = 75. To change the order of operations calculator , a vinculum (an over line or underline) was originally used. Today one uses parentheses (). Thus, if one wants to force addition to precede multiplication, one writes (3 + 4) × 5 = 35.

Let's see an example from algebra answers

Question:-

solve 24-(24+4+2)+2 x (4 x 2)

by using PEMDAS rule

Answer:-

In PEMDAS

P - Parentheses

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

let's solve the given equation step by step
in the same order ...

24-(30)+2 x (16)

24-32+30

combine the same terms

24+32-30

56 - 30

26 is the answer.

Simple quadratic equation

Topic: Quadratic Equation


An equation of the form ax²+bx+c=0 where a, b, c are real numbers and a =/ 0, is called a quadratic equation.

Question:

Solve: x2 - y = 3, x - y = -3

Answer:

   x2 - y = 3, x - y = -3

   x2 - y = 3

    x  - y = -3

    + y + y
    __________
    x = y - 3

  Putting this in the first equation

  (y -3)x2 - y = 3

 y2 - 6x + 9 - = 3

 y2 - 6x + 9 - y = 3

 y2 - 7y + 9 = 3

        -3    -3
        ____________

Factoring (y - 6) (y -1) = 0

         y = 6 on 1

         x = y - 3 = 6 - 3 = 3

         x = 1 - 3 = - 2

  The solution set is : {(-2,1) , (3,6)}