Perform the indicated operations and write in standard form.
Sq root of -25(3- sq root of -81)
Sorry, I don't know how to do the square root symbol.
I keep getting 15i-45i^2, which would be 45+15i in standard form, right? But my teacher says it's wrong, so what am I doing wrong? Thanks a lot, guys.
To simplify the expression and write it in standard form, let's break it down step by step.
Step 1: Simplify the square root of -81
The square root of -81 can be written as √(-1) * √(81). Since √(-1) is equal to "i", the square root of -81 can be simplified as 9i.
Step 2: Simplify -25(3 - √(-81))
Now, we can simplify the expression -25(3 - √(-81)) by substituting the simplified value of √(-81), which is 9i.
-25(3 - √(-81)) = -25(3 - 9i)
Step 3: Distribute the -25 into the parentheses
To distribute -25 into the parentheses, we multiply -25 with each term inside the parentheses.
-25(3 - 9i) = (-25*3) + (-25*(-9i))
Simplifying further, we get:
-75 + 225i
Therefore, the expression -25(3 - √(-81)) simplifies to -75 + 225i.
To simplify the expression √(-25)(3 - √(-81)), let's break it down step by step:
1. Start with simplifying the inside square root, √(-81):
Since the square root of a negative number is not a real number, we can rewrite it using the imaginary unit i: √(-81) = √(81) * √(-1) = 9i.
2. Now we have √(-25)(3 - 9i). Let's continue simplifying:
√(-25) can also be written as √(25) * √(-1) = 5i.
Plugging this back into the expression, we have: 5i(3 - 9i).
3. To simplify the expression with complex numbers, we can distribute the 5i to both terms inside the parentheses:
5i * 3 = 15i,
5i * (-9i) = -45i^2.
4. Finally, simplify -45i^2:
Remember that i^2 = -1. So, -45i^2 = -45 * (-1) = 45.
5. Combining the simplified terms, we have: 15i + 45.
Therefore, the expression √(-25)(3 - √(-81)) in standard form is 15i + 45.