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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PART A:
Scientific notation is given by A×10ⁿ where A is any number in a unit and 'n' is an integer.
0.000025 = 2.5×10⁻⁵
PART B:
Diameter of grain of sand ÷ Diameter of human body average cell
(2×10⁻⁴) ÷ (1×10⁻⁵)
(2÷1) × (10⁻⁴÷10⁻⁵)
2 × (10⁻⁴ ⁻ ⁻⁵) = 2 × 10⁽⁻⁴⁺⁵⁾ = 2 × 10¹ = 20 times bigger
PART C:
The diameter of human body's average cell in nanometer
1 × 10⁻⁵ metre = 1 × 10⁻⁵ × 10⁹ = 1 × 10⁽⁻⁵⁺⁹⁾ = 1 × 10⁴ nanometer
PART D:
Smallest bacteria = 300 nanometer
300 nm = 300 ÷ 10⁹ = (3 × 10²) ÷ 10⁹ = 3 × (10²⁻⁹) = 3 × 10⁻⁷ meter
PART E:
Laws of exponents that are applied in scientific notation is
xᵇ × xᵃ = x⁽ᵇ⁺ᵃ⁾
xᵇ ÷ xᵃ = x⁽ᵇ⁻ᵃ⁾
Answer:
<em>The simple interest is $11,212.5 and the equation to determine Josh's simple interest is I = PRT/100</em>
Step-by-step explanation:
The formula for calculating simple interest is expressed as;
SI = Principal * rate * time/100
SI = 50,000 * 6.9*39/100*12
SI = 500*6.9*39/12
SI = 134,550/12
SI = 11,212.5
<em>Hence the simple interest is $11,212.5 and the equation to determine Josh's simple interest is I = PRT/100</em>
P is the amount borrowed
R is the interest rate
T is the time in years
Standard Form: 79,031
Expanded Form: 70,000 + 9,000 + 30 + 1
Answer:
Is there any picture for it?
Step-by-step explanation:
