Simplify the number using the imaginary unit i. −144‾‾‾‾‾√

Mathematics

2 answers:

Sonbull [250]3 years ago

4 0

Answer:

12i

Step-by-step explanation:

The square root of 144 is 12 but the square root of a negative number results to an i after the real number.

Lilit [14]3 years ago

3 0

Assuming you mean sqrt(-144, we can use some properties of square roots to figure this out. sqrt(x*y) = sqrt(x) * sqrt(y)

We have sqrt(-1*144) = sqrt(-1) * sqrt(144). That would be i * 12, which is 12i.

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3 years ago

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Juli2301 [7.4K]

20 Answer: a₁ = 4

<u>Step-by-step explanation:</u>

$a_n=324,\ r=3,\ n=5\\\\a_n=a_1 \cdot r^{n-1}\\\\324=a_1\cdot 3^{5-1}\\\\\dfrac{324}{3^4}=a_1\\\\\dfrac{324}{81}=a_1\\\\\large\boxed{4}=a_1$

21 Answer: n = 13

<u>Step-by-step explanation:</u>

$a_n=\dfrac{1}{64},\ a_1=64,\ r=\dfrac{1}{2}\\\\a_n=a_1 \cdot r^{n-1}\\\\\dfrac{1}{64}=64\cdot \bigg(\dfrac{1}{2}\bigg)^{n-1}\\\\\dfrac{1}{64\cdot 64}=\bigg(\dfrac{1}{2}\bigg)^{n-1}\\\\\dfrac{1}{2^6\cdot 2^6}=\dfrac{1}{2^{n-1}}\\\\6+6=n-1\\\\\large\boxed{13}=n$

22 Answer: n = 5

<u>Step-by-step explanation:</u>

$a_n=48,\ a_1=1875\ r=\dfrac{2}{5}\\\\a_n=a_1 \cdot r^{n-1}\\\\48=1875\cdot \bigg(\dfrac{2}{5}\bigg)^{n-1}\\\\\dfrac{48}{1875}=\bigg(\dfrac{2}{5}\bigg)^{n-1}\\\\\dfrac{16}{625}=\bigg(\dfrac{2}{5}\bigg)^{n-1}}\\\\\bigg(\dfrac{2}{5}\bigg)^4=\bigg(\dfrac{2}{5}\bigg)^{n-1}}\\\\4=n-1\\\\\large\boxed{5}=n$