In this expression, "a + bi" represents a complex number, where "a" is the real part and "bi" is the imaginary part.
To calculate the product of two complex numbers in the form a + bi, you can use the FOIL method, where you multiply the first terms, the outer terms, the inner terms, and the last terms, and then combine like terms. For example, (2 + 3i)(4 + 5i) would become 2*4 + 2*5i + 3i*4 + 3i*5i, which simplifies to 8 + 10i + 12i + 15i^2. Finally, since i^2 is equal to -1, the final product would be 8 + 22i - 15, or -7 + 22i.
Yes, all numbers can be expressed in the form a + bi, including real numbers. This is because real numbers can be written as a complex number with a zero imaginary part. For example, the number 5 can be written as 5 + 0i.
The "a + bi" form is a standard way of representing complex numbers because it allows us to easily distinguish between the real and imaginary parts. It also helps with performing operations on complex numbers, such as addition, subtraction, multiplication, and division.
Yes, the product of two complex numbers can also be expressed in the form r(cosθ + isinθ), where r is the magnitude of the complex number and θ is the angle it makes with the positive real axis. This is known as the polar form of a complex number.