Question

An example of classes with complex numbers, calculator, ask if complex or real then plot path, BEDMAS.

Answer 1

A complex number is a number of the form (a+bi) where

• a is the real part of the complex number.
• bi is the imaginary part of the complex number.

If b=0, then a+bi is a real number. If a=0 and b are not equal to 0, the complex number is called an imaginary number. An imaginary number is an even root of a negative number.

Basic operations with complex numbers :
1) Addition
Very simple, add up the real parts (without i) and add up the imaginary parts (with i):
This is equal to use rule:

2) Subtraction
Again very simple, subtract the real parts and subtract the imaginary parts (with i):
This is equal to use rule:

3) Multiplication
To multiply two complex number use distributive law, avoid binomials and apply i2 = -1.
This is equal to use rule:

4) Division
Division of two complex number is based on avoiding imaginary unit i from the denominator. This can be done only via i2 = -1. If the denominator is c+di, to make it without i (or make it real), just multiply with conjugate c-di:


5) Absolute value or modulus
Absolute value or modulus is the distance of image of complex number from an origin in the plane. That use the Pythagorean theorem, just as case of the 2D vector. Very simple, see examples: _.

BEDMAS acronyms that help individuals remember how to perform a set of procedure in math. BEDMAS (otherwise known as PEMDAS) is one of them.BEDMAS/PEMDAS refer to following the order of operations Brackets / Parentheses, Exponents, Division, Multiplication, Addition, Subtraction. Brackets/Parentheses always come first and exponents come second. When working with multiplication and division, you do whichever comes first as you work from left to right. If multiplication comes first, do it before dividing. The same holds true for addition and subtraction, when the subtraction comes first, subtract before you add.

Example:-

Solution

Step 1: Add: 1 + i = 1+i
Step 2: Multiple: 5 * (the result of step No. 1) = 5 * (1+i) = 5 * 1 + 5 * i = 5+5i = 5 +i(5)
Step 3: Subtract: -2 - 5i = -2-5i
Step 4:. Exponentiation: (the result of step No. 3) ² = (-2-5i) ² = (-2-5i) * (-2-5i) = -2 * (-2) + (-2) * (-5i) + (-5i) * (-2) + (-5i) * (-5i) = 4+10i+10i+25i² = 4+10i+10i-25 = 4 - 25 +i(10 + 10) = -21+20i
Step 5: Multiple: (the result of step No. 2) * (the result of step No. 4) = (5+5i) * (-21+20i) = 5 * (-21) + 5 * 20i + 5i * (-21) + 5i * 20i = -105+100i-105i+100i² = -105+100i-105i-100 = -105 - 100 +i(100 - 105) = -205-5i

Hence, Rectangular form: z = -205-5i

Cartesian coordinates:
Real part: Re z = x = -205
Imaginary part: Im z = y = -5

How to plot graph:-

• Determine the real part and the imaginary part of the complex number.
• Move along the horizontal axis to show the real part of the number.
• Move parallel to the vertical axis to show the imaginary part of the number.
• Plot the point.