(10 Squar root -13)(-5 square root -5)
put in standard form a+bi
I really don't understand square roots so can you show me how to do these please
by definition √-1 = i
so rewrite
(10√-13)(-5√-5) as
(10√-1√13)(-5√-i√5)
= (10i√13)(-5i√5)
= -50i^2√65
= +50√5
To simplify the expression (10√-13)(-5√-5), we need to simplify each square root separately and then multiply the simplified expressions.
First, let's simplify the square root of -13:
√-13 can be written as √(-1 * 13). Since the square root of -1 is denoted as "i," we have:
√(-1 * 13) = √-1 * √13 = i√13.
Next, let's simplify the square root of -5:
√-5 can be written as √(-1 * 5). Using the same reasoning as before, we have:
√(-1 * 5) = √-1 * √5 = i√5.
Now, we can multiply the simplified expressions:
(10√-13)(-5√-5) = (10i√13)(-5i√5).
To multiply these, we can apply the associative and commutative properties of multiplication and simplify:
(10i√13)(-5i√5) = -50i^2√(13 * 5) = -50(-1)√65 = 50√65.
So, the simplified expression in standard form is 50√65.
To simplify the expression (10√-13)(-5√-5) and write it in standard form a + bi, we need to remember the properties of the square root of negative numbers, which involves using the imaginary unit, i.
1. Start by simplifying the square roots of negative numbers:
- √-13 = √13 * √-1
- √-5 = √5 * √-1
2. Apply the property √-1 = i.
- √-13 = √13 * i
- √-5 = √5 * i
After this step, the expression becomes:
(10√13 * i)(-5√5 * i)
3. Multiply the real parts together (10√13 * -5√5) and the imaginary parts together (i * i).
- The real parts: 10 * -5 = -50
- The imaginary parts: i * i = i^2. Remember that i^2 is equal to -1.
The expression becomes: -50√13 * √5 * i^2
4. Simplify further.
- √13 * √5 = √(13 * 5) = √65
Replace i^2 with -1:
-50√65 * -1
5. Apply the property of i^2 = -1. Multiply both terms by -1.
-50√65 * -1 = 50√65
So the expression (10√-13)(-5√-5) simplifies to 50√65.
Written in standard form a + bi, where a is the real part and b is the imaginary part:
a = 0, since there is no real part in 50√65
b = 50√65
Therefore, the simplified expression in standard form is 0 + 50√65i.