Question 163808: Write in standard form 3-sqrt(-27)
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website! Write in standard form 3-sqrt(-27).
The standard form for complex numbers must be in the form a + bi,
where a = the real number and bi = the imaginary number.
Keep in mind that we cannot take the square root of a negative number.
This does not exist in the world of math. In your math book, it is called UNDEFINED, which means does not exist.
So, mathematicians came up with the letter i to represent sqrt{-1}.
So, i = sqrt{-1}. This you must memorize. Trust me, it will make your life dealing with complex numbers so much easier.
You were given sqrt{-27}, which = sqrt{3} times sqrt{9} times sqrt{-1}.
As you know, the sqrt{3} cannot be reduced must further because it is already in lowest terms.
The sqrt{9} = 3, as you already know.
The sqrt{-1} = i like I said above.
We now put it all together leaving the letter i outside the sqrt{3} on the right side.
Your final answer is: 3 - 3(sqrt{3})i
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In your answer, the number 3 alone is the real number and 3(sqrt{3})i is the imaginary number. Can you see how the final answer is written in the
form a + bi?
Is this clear?
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