Express the following in the form a + bi, where a and b are real numbers:

√15+8i
√3-4i
√2i
√-48+14i

For the last one square root of -48+14i is

1,2
Bc it says I got it right

To express the complex numbers in the form a + bi, where a and b are real numbers, we use the following steps:

1. Write down the complex number.
2. Identify the real part and the imaginary part.
3. Express both parts in their simplest forms.
4. Combine the real part and the imaginary part using the format a + bi.

Let's apply these steps to the given complex numbers:

1. √15+8i
- Real part: √15
- Imaginary part: 8i
- Combine: √15 + 8i

2. √3-4i
- Real part: √3
- Imaginary part: -4i (Note: The 'i' is negative here)
- Combine: √3 - 4i

3. √2i
- Real part: 0 (because √2 multiplied by any real number is still 0)
- Imaginary part: √2i
- Combine: √2i (Note: There is no real part, so it is expressed as √2i)

4. √-48+14i
- Real part: 0 (because the square root of a negative number is not real)
- Imaginary part: -√48 + 14i (Note: The 'i' is positive here)
- Combine: -√48 + 14i

Therefore, the expressions in the form a + bi are:
- √15 + 8i
- √3 - 4i
- √2i
- -√48 + 14i

To express a complex number in the form a + bi, where a and b are real numbers:

1. Determine the real part of the complex number. This is the number outside the square root symbol.
2. Determine the imaginary part of the complex number. This is the number multiplied by the imaginary unit, i, inside the square root symbol.

Now let's apply this to each of the given complex numbers:

1. √15 + 8i:
The real part is √15, and the imaginary part is 8.
So, the complex number can be expressed as √15 + 8i.

2. √3 - 4i:
The real part is √3, and the imaginary part is -4.
So, the complex number can be expressed as √3 - 4i.

3. √2i:
To simplify this, first express i as √-1.
Now, we can rewrite the complex number as √2 * √-1.
Since √-1 is equal to i, the complex number can be expressed as √2i.

4. √-48 + 14i:
The real part is √-48, which can be simplified as √(-1) * √48.
Since √(-1) is equal to i, and √48 is equal to 4√3, the real part can be expressed as 4√3i.
The imaginary part is 14.
So, the complex number can be expressed as 4√3i + 14i.

Note: Simplifying the square root of a negative number requires the use of imaginary unit, i, which is defined as √-1.

The first 3 are already expressed in the form a + bi

for the last one:
√-48 + 14i
= 4√3 i + 14i
= 0 + (4√3+14) i