Which of the following is equal to the expression?
(3i)²
(3i)² = 3i * 3i = 9i²
Note that i² is equal to -1, so 9i² = 9(-1) = -9
Which of the following is equal to the expression (3i)²
a) -9
b) -9i
c) 9
d) 9i
The correct answer is a) -9.
To find the value of (3i)², we can begin by using the property of exponents that states (a * b)² = a² * b².
In this case, a = 3 and b = i. Therefore, (3i)² = 3² * i².
Now, let's calculate the values of 3² and i² separately.
First, 3² = 3 * 3 = 9.
Next, i² represents the square of the imaginary unit i. The imaginary unit i is defined as √(-1), so i² = (√(-1))² = -1.
Substituting these values back into the expression, we have (3i)² = 9 * (-1).
Finally, multiplying 9 and -1, we get:
(3i)² = -9.
Therefore, the value of the expression (3i)² is -9.