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:
$7500
Step-by-step explanation:
$5000 was deposited
5% annual interest of the $5000 is $250
so in ten years the interest will be 10 ×$250 =$2500
so the total sum that will be in the account is $5000 + $2500 =$7500
The answer is D.
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Answer:
Step-by-step explanation:
B just took the until test
Answer:
= 5n - 2
Step-by-step explanation:
The nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₄ = 18 , then
a₁ + 3d = 18 , that is
3 + 3d = 18 ( subtract 3 from both sides )
3d = 15 (divide both sides by 3 )
d = 5
Then
= 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2 ← explicit rule