Evaluate the expression sqrt(-6)/(sqrt(-3) sqrt(-4)) and write the result in the form a+bi

Evaluate the expression sqrt(-6)/(sqrt(-3) sqrt(-4)) and write the result in the form a+bi

Question
Evaluate the expression \(\displaystyle\frac{\sqrt{{-{6}}}}{{\sqrt{{-{3}}}\sqrt{{-{4}}}}}\) and write the result in the form a+bi

Answers (1)

2021-01-03
\(\displaystyle{i}\frac{\sqrt{{6}}}{{{i}\sqrt{{3}}\cdot{i}\sqrt{{4}}}}=-{i}\frac{\sqrt{{6}}}{{2}}\sqrt{{3}}=-{i}\frac{\sqrt{{\frac{{6}}{{3}}}}}{{2}}=-{i}\frac{\sqrt{{2}}}{{2}}\). So \(\displaystyle{a}={0}{\quad\text{and}\quad}{b}=-\frac{\sqrt{{2}}}{{2}}\) for a+ib.
Therefore \(\displaystyle{a}={0}{\quad\text{and}\quad}{b}=-√\frac{{2}}{{2}}{\quad\text{or}\quad}-\frac{{1}}{
0

Relevant Questions

asked 2021-02-13
Is the algebraic expression a polynomial? If it is,write the polynomial in standard form.
\(\displaystyle{x}^{{{2}}}-{x}^{{{3}}}+{x}^{{{4}}}-{5}\)
asked 2021-06-03
Determine whether the following function is a polynomial function. If the function is a polynomial​ function, state its degree. If it is​ not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.
\(g(x)=3-\frac{x^{2}}{4}\)
asked 2021-06-04
Determine whether \(F(x)=5x^{4}-\pi x^{3}+\frac{1}{2}\) is a polynomial. If it is, state its degree. If not, say why it is not a polynomial. If it is a polynomial, write it in standard form. Identify the leading term and the constant term.
asked 2020-12-24
a student is speeding down route 11 in his fancy red Porschewhen his radar system warns him of an obstacle 400 ft ahead. heimmediately applies the brakes, starts to slow down and spots askunk in the road directly ahead of him. the "black box" in thePorsche records the car's speed every 2 seconds , producing thefollowing table. the speed decreases throughout the 10 seconds ittakes to stop, although not necessarily at a uniform rate.
time since brakes applied (sec) 0 2 4 6 8 10
speed(ft/sec) 100 80 50 25 10 0
a) what is your best estimate of the total distance thestudent's car travelled before coming to rest?
b) which one of the following statements can you justify fromthe information given?
1) the car stopped before getting to the skunk.
2) the " black box" data is inconclusive. the skunk may or maynot have been hit.
3) the skunk was hit by the car.
asked 2021-04-06
Find all rational zeros of the polynomial, and write the polynomial in factored form.
\(\displaystyle{P}{\left({x}\right)}={6}{x}^{{{4}}}-{23}{x}^{{{3}}}-{13}{x}^{{{2}}}+{32}{x}+{16}\)
asked 2021-03-20
Find all rational zeros of the polynomial, and write the polynomial in factored form.
\(\displaystyle{P}{\left({x}\right)}={6}{x}^{{{4}}}-{7}{x}^{{{3}}}-{12}{x}^{{{2}}}+{3}{x}+{2}\)
asked 2021-05-20
Find all rational zeros of the polynomial, and write the polynomial in factored form.
\(\displaystyle{P}{\left({x}\right)}={3}{x}^{{{5}}}-{14}{x}^{{{4}}}-{14}{x}^{{{3}}}+{36}{x}^{{{2}}}+{43}{x}+{10}\)
asked 2021-03-03
Find all rational zeros of the polynomial, and write the polynomial in factored form.
\(\displaystyle{P}{\left({x}\right)}={2}{x}^{{{3}}}+{7}{x}^{{{2}}}+{4}{x}-{4}\)
asked 2021-04-25
The value of the expression [9]+[11] in \(\displaystyle{Z}_{{{15}}}\) and to write the answer in the form [r] with \(\displaystyle{0}\leq{r}{<}{m}\).
asked 2021-05-08
The value of the expression [5]+[10] in \(\displaystyle{Z}_{{{11}}}\) and to write the answer in the form [r] with \(\displaystyle{0}\leq{r}{<}{m}\).
...