Which of the following re-expresses the negative square root −5−20−−−−√%0D%0A−%0D%0A5%0D%0A−%0D%0A20%0D%0A as a complex number in the standard form a+bi?(1 point)%0D%0AResponses%0D%0A%0D%0A−5i5–√%0D%0A−%0D%0A5%0D%0A𝑖%0D%0A5%0D%0Anegative 5 i square root of 5%0D%0A%0D%0A−10i5–√%0D%0A−%0D%0A10%0D%0A𝑖%0D%0A5%0D%0Anegative 10 i square root of 5%0D%0A%0D%0A5i10−−√%0D%0A5%0D%0A𝑖%0D%0A10%0D%0A5 i square root of 10%0D%0A%0D%0A−20i5–√

Question

Which of the following re-expresses the negative square root  −5−20−−−−√%0D%0A−%0D%0A5%0D%0A−%0D%0A20%0D%0A  as a complex number in the standard form a+bi?(1 point)%0D%0AResponses%0D%0A%0D%0A−5i5–√%0D%0A−%0D%0A5%0D%0A𝑖%0D%0A5%0D%0Anegative 5 i square root of 5%0D%0A%0D%0A−10i5–√%0D%0A−%0D%0A10%0D%0A𝑖%0D%0A5%0D%0Anegative 10 i square root of 5%0D%0A%0D%0A5i10−−√%0D%0A5%0D%0A𝑖%0D%0A10%0D%0A5 i square root of 10%0D%0A%0D%0A−20i5–√

GPT-4o mini · Answer

To re-express the expression $-\sqrt{-5 - 20}$ as a complex number in the standard form $a + bi$, we start by simplifying the square root. First, calculate the expression under the square root: $$ -5 - 20 = -25 $$ Now we have: $$ -\sqrt{-25} $$ The square root of a negative number can be expressed using the imaginary unit $i$, where $i = \sqrt{-1}$. Thus, we can rewrite the square root: $$ \sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i $$ So we have: $$ -\sqrt{-25} = -5i $$ Thus, the expression $-\sqrt{-5 - 20}$ simplifies to: $$ -5i $$ This can be expressed in standard form $a + bi$ as: $$ 0 - 5i $$ Therefore, the answer is: $-5i$