Overview: 5 questions will be solved this time.Among them
☆3 equations
☆1 arithmetic calculations
☆1 integer calculations
[ 1/5 Equation]
Work: Find the solution of equation [3+4i]/[1-2i]-[-1+4] = 0 .
Question type: Equation
Solution:Original question:| | ( | 3 | + | 4 | i | ) | ÷ | ( | 1 | − | 2 | i | ) | − | ( | - | 1 | + | 4 | ) | = | 0 |
| Multiply both sides of the equation by: | ( | 1 | − | 2 | i | ) |
| | ( | 3 | + | 4 | i | ) | − | ( | - | 1 | + | 4 | ) | ( | 1 | − | 2 | i | ) | = | 0 |
Remove a bracket on the left of the equation::
| | 3 | + | 4 | i | − | ( | - | 1 | + | 4 | ) | ( | 1 | − | 2 | i | ) | = | 0 |
Remove a bracket on the left of the equation:
| | 3 | + | 4 | i | + | 1 | ( | 1 | − | 2 | i | ) | − | 4 | ( | 1 | − | 2 | i | ) | = | 0 |
Remove a bracket on the left of the equation:
| | 3 | + | 4 | i | + | 1 | × | 1 | − | 1 | × | 2 | i | − | 4 | ( | 1 | − | 2 | i | ) | = | 0 |
The equation is reduced to :
| | 3 | + | 4 | i | + | 1 | − | 2 | i | − | 4 | ( | 1 | − | 2 | i | ) | = | 0 |
The equation is reduced to :
| | 4 | + | 2 | i | − | 4 | ( | 1 | − | 2 | i | ) | = | 0 |
Remove a bracket on the left of the equation:
| | 4 | + | 2 | i | − | 4 | × | 1 | + | 4 | × | 2 | i | = | 0 |
The equation is reduced to :
The equation is reduced to :
The coefficient of the unknown number is reduced to 1 :
We obtained :
This is the solution of the equation.
[2/% Digital analysis]
Assignment: Convert 200/40 to decimal.
Question type: Convert fraction to decimal
Solution:
First reduce fraction:
The numerator and denominator of the fraction 200/40 are reduced to the simplest fraction by the common divisor 2,2,2,5,
is: 5/1
5/1=5 *Note: Can be converted to integer.[3/5 Formula]
Work: Calculate the value of equation 160+40*20 .
Question type: Mathematical calculation
Solution:
160+40*20
=160+800
=960 Answer:160+40*20=960[ 4/5 Equation]
Work: Find the solution of equation [1+i]*[2+4i]+[-3+i] = 0 .
Question type: Equation
Solution:Original question:| | ( | 1 | + | i | ) | ( | 2 | + | 4 | i | ) | + | ( | - | 3 | + | i | ) | = | 0 |
Remove the bracket on the left of the equation:
| Left side of the equation = | 1 | ( | 2 | + | 4 | i | ) | + | i | ( | 2 | + | 4 | i | ) | + | ( | - | 3 | + | i | ) |
| = | 1 | × | 2 | + | 1 | × | 4 | i | + | i | ( | 2 | + | 4 | i | ) | + | ( | - | 3 | + | i | ) |
| = | 2 | + | 4 | i | + | i | ( | 2 | + | 4 | i | ) | + | ( | - | 3 | + | i | ) |
| = | 2 | + | 4 | i | + | i | × | 2 | + | i | × | 4 | i | + | ( | - | 3 | + | i | ) |
| = | 2 | + | 6 | i | + | i | × | 4 | i | + | ( | - | 3 | + | i | ) |
| = | 2 | + | 6 | i | + | i | × | 4 | i | − | 3 | + | i |
The equation is transformed into :
The solution of the equation:
i1≈-1.882782 , keep 6 decimal places
i2≈0.132782 , keep 6 decimal places
There are 2 solution(s).
解程的详细方法请参阅:《方程的解法》[ 5/5 Equation]
Work: Find the solution of equation a+2a = 0 .
Question type: Equation
Solution:Original question:| Left side of the equation = | 3 | a |
The equation is transformed into :
The coefficient of the unknown number is reduced to 1 :
We obtained :
This is the solution of the equation.
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