Question

Evaluate the expression √-9 √-36 and write the result in the form a+bi
The real number a equals
The real number b equals

Answer 1

To evaluate the expression \( \sqrt{-9} \cdot \sqrt{-36} \), we can first rewrite the square roots of negative numbers using the imaginary unit \( i \), where \( i = \sqrt{-1} \).

1. Calculate \( \sqrt{-9} \):
\[
\sqrt{-9} = \sqrt{9} \cdot \sqrt{-1} = 3i
\]

2. Calculate \( \sqrt{-36} \):
\[
\sqrt{-36} = \sqrt{36} \cdot \sqrt{-1} = 6i
\]

3. Now multiply the two results:
\[
\sqrt{-9} \cdot \sqrt{-36} = (3i) \cdot (6i) = 18i^2
\]

4. Since \( i^2 = -1 \), we can substitute that in:
\[
18i^2 = 18(-1) = -18
\]

Thus, the result of the expression \( \sqrt{-9} \cdot \sqrt{-36} \) is:
\[
-18 + 0i
\]

In the form \( a + bi \):
- The real number \( a = -18 \)
- The real number \( b = 0 \)

So, we have:
- The real number \( a \) equals \( -18 \)
- The real number \( b \) equals \( 0 \)