Both bots got this wrong:
Which of the following re-expresses the negative square root -6√-20 as a complex number in the standard form a + bi?
-12i√5
-12√5
2i√5
-12√5i
since √20 = 2√5, -6√-20 = -6 * 2√5 i = -12√5 i
the 2nd bot missed this because it interpreted √5i as √(5i) rather than (√5)i
The correct re-expression of the negative square root -6√-20 as a complex number in standard form is -12√5i.
To re-express the negative square root -6√-20 as a complex number in the standard form a + bi, we can start by simplifying the square root.
√-20 = √((-1) * 4 * 5) = √(4 * -1) * √5 = 2i√5
Now we can substitute this value back into the expression.
-6√-20 = -6 * 2i√5 = -12i√5
Therefore, the re-expression in the standard form a + bi is -12i√5.
To re-express the negative square root -6√-20 as a complex number in the standard form a + bi, we can follow these steps:
Step 1: Simplify the square root expression √(-20).
Since the square root of a negative number is not a real number, we need to express it as a complex number by introducing the imaginary unit i.
√(-20) = √(20) * i = √(4 * 5) * i = 2√5 * i.
Step 2: Multiply -6 by 2√5 * i to obtain the final answer.
-6√(-20) = -6 * 2√5 * i = -12√5 * i.
Therefore, the correct answer is -12√5i.