What is (-3+ the square root of -25) - (4+ square root of -16)
the product of 8 and a number is 56, what is 2 less than the number?
Your problem:
(-3 + √-25) - (4 + √-16)
Working this out:
-3 + 5i - 4 - 4i
-7 + i
And that's as far as you can go to simplify here.
I hope this will help.
To solve the expression (-3 + √-25) - (4 + √-16), we need to simplify each term separately before subtracting them.
Let's start with the first term, -3 + √-25. To find the square root of -25, we need to express it in terms of the imaginary unit i, where i is defined as the square root of -1.
√-25 = √(25 * -1) = √25 * √-1 = 5i
Therefore, -3 + √-25 becomes -3 + 5i.
Moving on to the second term, 4 + √-16. Similar to before, we express the square root of -16 in terms of i.
√-16 = √(16 * -1) = √16 * √-1 = 4i
Hence, 4 + √-16 simplifies to 4 + 4i.
Now, we can subtract these two simplified terms:
(-3 + 5i) - (4 + 4i)
Combine the real numbers and the imaginary numbers separately:
-3 - 4 + (5i - 4i)
Simplify further:
-7 + i
Therefore, the expression (-3 + √-25) - (4 + √-16) simplifies to -7 + i.
Following the same instructions, we can solve the second problem:
The product of 8 and a number is 56. Let's denote the number as x.
8 * x = 56
To find the value of x, we divide both sides of the equation by 8:
x = 56 / 8
Simplifying the right side gives:
x = 7
To find 2 less than the number, we subtract 2 from the value of x:
7 - 2 = 5
Therefore, 2 less than the number is 5.