SOLUTION: Hi I need help with these questions: 1. -9+i/-9-3i I divided the num and dem by the recip -9+3i and then used FOIL is that correct then simplified My answer was 13/15-3i/

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Hi I need help with these questions: 1. -9+i/-9-3i I divided the num and dem by the recip -9+3i and then used FOIL is that correct then simplified My answer was 13/15-3i/      Log On


   

Question 211101: Hi I need help with these questions:
1. -9+i/-9-3i I divided the num and dem by the recip -9+3i and then used FOIL is that correct then simplified My answer was 13/15-3i/15 help
2. x^-6x+17=0 Do I use the quadr formula to solve this I did and got 4-i and 4+i
3. (x^+3x)+5=0 help my ans were not close to the choices I had (also noted is problem that I=sqrt of 1)
4. (x^-2x)+7=0 help my ans were not close to the choices I had (also noted is problem that I=sqrt of 1)
5. (x^+2x)+7=0 help my ans were not close to the choices I had (also noted is problem that I=sqrt of 1)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first three to get you going. The rest will be like # 2 and # 3

# 1


%28-9%2Bi%29%2F%28-9-3i%29 Start with the given expression.


%28%28-9%2Bi%29%2F%28-9-3i%29%29%28%28-9%2B3i%29%2F%28-9%2B3i%29%29 Multiply the fraction by %28-9%2B3i%29%2F%28-9%2B3i%29.


Note: -9%2B3i is the complex conjugate of -9-3i. Multiplying two conjugate pairs will result in a real number.


%28%28-9%2Bi%29%28-9%2B3i%29%29%2F%28%28-9-3i%29%28-9%2B3i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%2881-27i-9i%2B3i%5E2%29%2F%2881-27i%2B27i-9i%5E2%29 Multiply.


%2881-27i-9i%2B3i%5E2%29%2F%2881-27i%2B27i-9%28-1%29%29 Replace i%5E2 with -1


%2881-27i-9i%2B3i%5E2%29%2F%2881-27i%2B27i%2B9%29 Multiply


%2878-36i%29%2F%2890%29 Combine like terms.


%2878%29%2F%2890%29%2B%28%28-36%29%2F%2890%29%29i Break up the fraction.


13%2F15-%282%2F5%29i Reduce.


So %28-9%2Bi%29%2F%28-9-3i%29=13%2F15-%282%2F5%29i.


So the expression is now in standard form a%2Bbi where a=13%2F15 and b=-2%2F5




# 2




x%5E2-6x%2B17=0 Start with the given equation.


Notice that the quadratic x%5E2-6x%2B17 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-6, and C=17


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%2817%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-6, and C=17


x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%2817%29+%29%29%2F%282%281%29%29 Negate -6 to get 6.


x+=+%286+%2B-+sqrt%28+36-4%281%29%2817%29+%29%29%2F%282%281%29%29 Square -6 to get 36.


x+=+%286+%2B-+sqrt%28+36-68+%29%29%2F%282%281%29%29 Multiply 4%281%29%2817%29 to get 68


x+=+%286+%2B-+sqrt%28+-32+%29%29%2F%282%281%29%29 Subtract 68 from 36 to get -32


x+=+%286+%2B-+sqrt%28+-32+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%286+%2B-+4i%2Asqrt%282%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%286%29%2F%282%29+%2B-+%284i%2Asqrt%282%29%29%2F%282%29 Break up the fraction.


x+=+3+%2B-+2%2Asqrt%282%29%2Ai Reduce.


x+=+3%2B2%2Asqrt%282%29%2Ai or x+=+3-2%2Asqrt%282%29%2Ai Break up the expression.


So the solutions are x+=+3%2B2%2Asqrt%282%29%2Ai or x+=+3-2%2Asqrt%282%29%2Ai



# 3

x%5E2%2B3x%2B5=0 Start with the given equation.


Notice that the quadratic x%5E2%2B3x%2B5 is in the form of Ax%5E2%2BBx%2BC where A=1, B=3, and C=5


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%283%29+%2B-+sqrt%28+%283%29%5E2-4%281%29%285%29+%29%29%2F%282%281%29%29 Plug in A=1, B=3, and C=5


x+=+%28-3+%2B-+sqrt%28+9-4%281%29%285%29+%29%29%2F%282%281%29%29 Square 3 to get 9.


x+=+%28-3+%2B-+sqrt%28+9-20+%29%29%2F%282%281%29%29 Multiply 4%281%29%285%29 to get 20


x+=+%28-3+%2B-+sqrt%28+-11+%29%29%2F%282%281%29%29 Subtract 20 from 9 to get -11


x+=+%28-3+%2B-+sqrt%28+-11+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-3+%2B-+i%2Asqrt%2811%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-3%2Bi%2Asqrt%2811%29%29%2F%282%29 or x+=+%28-3-i%2Asqrt%2811%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%28-3%2Bi%2Asqrt%2811%29%29%2F%282%29 or x+=+%28-3-i%2Asqrt%2811%29%29%2F%282%29