The product of a <em>complex</em> number and its conjugate is (a + i b) · (a - i b), where a and b are <em>real</em> numbers, and the result for the <em>complex</em> number 2 + i 3 is 13.
<h3>What is the multiplication of a complex number and its conjugate</h3>
Let be a <em>complex</em> number a + i b, whose conjugate is a - i b. Where a and b are <em>real</em> numbers. The product of these two numbers is:
(a + i b) · (a - i b)
Then, we proceed to obtain the result by some algebraic handling:
a · (a + i b) + (- i b) · (a + i b)
a² + i a · b - i a · b - i² b²
a² - i² b²
a² + b²
If we know that a = 2 and b = 3, then the product of the complex number and its conjugate is:
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Answer:
Range is 18.
Step-by-step explanation:
Range can be calculated by subtracting the smallest value of the data set from the largest value of the data set.
The values are:
13, 17, 18, 15, 12, 21, 10, 6, 8, 11, 3
Largest Value in this data set: 21
Smallest Value in this data set: 3
Range = Largest Value - Smallest Value
Range = 21 - 3
Range = 18
Area of ∆=1/2bh
80yd^2=1/2(b)(10yd)
80yd^2=5yd(b)
80yd^2÷5yd=b
16yd=b
Slope intercept form of a line is y=mx+b where m= slope and b=y-intercept.
Now compare this form with the tiven equation y=4x-9 to get the value of m.
So, m= 4.
Slope of all parallel lines are always equal. Which means the line which is parallel to this has also the same slope: m=4.
Now we need to find the value of b to get the equation. That parallel line passes through (-5,3).
The point intercept form of a line is,
(y-y1)=m(x-x1)
So, we can plug in the m=4, x1=-5 and y1=3 in the above equation. Hence,
y-3=4(x-(-5))
y-3=4(x+5) Since -(-5)=+5
y-3=4x+20 By distributing property.
y=4x+20+3 Adding 3 to each sides.
y=4x+23
So, the slope-intercept form of that parallel line is y=4x+23.
Answer:
The sum of 5x and 2xis at least 14 as an inequality is: 5x +2x < 14
The product of x and y is less than 4 as an inequality is: x * y < 4
Step-by-step explanation:
