Which of the following shows an expression equivalent to the product of two complex numbers, 5i * 4i?
The product of two complex numbers, 5i * 4i, can be calculated by multiplying the real parts and the imaginary parts separately.
The real part of 5i is 0, and the real part of 4i is also 0. So, their product will have a real part of 0.
The imaginary part of 5i is 5, and the imaginary part of 4i is 4. So, their product will have an imaginary part of -20.
Therefore, the expression that represents the product of two complex numbers 5i * 4i is 0 - 20i, which is equivalent to -20i.
To find the product of two complex numbers, you can use the distributive property and the fact that the imaginary unit \(i\) satisfies the equation \(i^2 = -1\).
Let's solve the expression \(5i \times 4i\) step by step:
1. Start by multiplying the two imaginary parts: \(i \times i\).
Since \(i^2 = -1\), we can substitute \(-1\) for \(i^2\):
\(i \times i = -1\)
2. Next, multiply the two real parts: \(5 \times 4 = 20\).
3. Combine the real and imaginary parts:
The result is the product of the real parts minus the product of the imaginary parts.
\(20 - 1 = 19\)
Therefore, the expression \(5i \times 4i\) is equivalent to \(19\).
To find the product of two complex numbers (in this case, 5i * 4i), we need to use the fact that the imaginary unit i satisfies the property i^2 = -1.
We know that i*i = -1, so we can rewrite the expression 5i * 4i as:
5i * 4i = (5 * 4) * (i * i)
Now, we can simplify the expression:
(5 * 4) * (i * i) = 20 * (i * i)
Since i * i = -1, we substitute this value in:
20 * (i * i) = 20 * (-1)
Finally:
20 * (-1) = -20
Therefore, the product of 5i * 4i is -20.