A student has simplified the following expression incorrectly.
Identify the mistake that was made and simplify the expression correctly. Show all necessary steps in the space provided.
(−3i)(−5i)
15i
The student made an error when multiplying the imaginary units. The correct way to simplify the expression is as follows:
(−3i)(−5i)
= (-3)(-5)(i)(i)
= 15i²
Since i² is equal to -1, we can simplify further:
= 15(-1)
= -15
Therefore, the correct simplified expression is -15.
To simplify the expression (-3i)(-5i), the student made the mistake of not multiplying the coefficients and the imaginary parts separately. They only multiplied the coefficients, resulting in 15, and ignored the fact that both terms have an imaginary part, represented by the letter "i".
To simplify the expression correctly, we need to multiply both the coefficients and the imaginary parts separately. Here are the step-by-step calculations:
(-3i)(-5i)
First, let's multiply the coefficients: -3 x -5 = 15.
Next, let's multiply the imaginary part: i x i = i^2.
Since i^2 is defined as -1, we have i^2 = -1.
Now we can combine the results of the coefficient multiplication and the imaginary part:
15 x -1 = -15.
Thus, the correct simplification of the expression (-3i)(-5i) is -15.
To simplify the expression (−3i)(−5i), we need to multiply the two complex numbers together.
When multiplying two complex numbers, we can use the following rule: i^2 = -1.
Using this rule, we can simplify the expression as follows:
(−3i)(−5i) = (-3 * -5) * (i * i)
= 15 * (i * i)
= 15 * (-1)
= -15
Therefore, the correct simplified expression is -15.
The student made a mistake by incorrectly applying the rule i^2 = -1. They should have simplified the product of i as i * i = (i^2) = -1.