**WILL MARK BRAINLEIST FOR TRUE ANSWERS!!!** 7th Grade Math
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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:
To learn more on complex numbers: brainly.com/question/10251853
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The exponential regression equation is y = 172.21(0.99)ˣ and at x = 60 minutes y = 94.22 degree Fahrenheit and at x = 240 minutes y = 15.43 degree Fahrenheit.
<h3>What is correlation?</h3>It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
We have data shown in the table:
We can find the exponential regression equation using the data shown.
After calculating from the data:
a = 172.21 and b = 0.99
The correlation coefficient will be:
r = -0.99
The range will be all real numbers.
The domain will be y > 0
As we can see in the graph x ∈R and y>0
After an hour,
Plug x = 60 minutes in the exponential regression equation:
y = 94.22 degree Fahrenheit
After 4 hours, plug x = 240
y = 15.43 degree Fahrenheit
Similarly, we can find any data from the exponential regression equation.
Thus, the exponential regression equation is y = 172.21(0.99)ˣ and at x = 60 minutes y = 94.22 degree Fahrenheit and at x = 240 minutes y = 15.43 degree Fahrenheit.
Learn more about the correlation here:
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