SOLUTION: square root of 18x2 multiplied by the square root of 12x 2) Divide 3+2i/1-1i 3) Write a quadratic equation whose solutions are 3+i and 3-i

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: square root of 18x2 multiplied by the square root of 12x 2) Divide 3+2i/1-1i 3) Write a quadratic equation whose solutions are 3+i and 3-i      Log On


   

Question 38549: square root of 18x2 multiplied by the square root of 12x

2) Divide 3+2i/1-1i

3) Write a quadratic equation whose solutions are 3+i and 3-i
Answer by tran3209(100) About Me  (Show Source):
You can put this solution on YOUR website!
(sqrt18X^2)(sqrt12x)--->(sqrt2.3^2X^2)(sqrt3.2^2X)--->(3Xsqrt2)(2sqrt3X)
This is the answer: 6Xsqrt6X
3+2i/1-i multiply the numerator & the denominator by the conjugate of 1-i: 1+i
(3+2i)(1+i)/(1-i)(1+i)Apply the formula A^2-B^2=(A+B)(A-B)in the denominator
3+3i+2i+2i^2/1-i^2 Replace i^2 by -1
3+5i+2(-1)/1-(-1)---->3+5i-2/1+1--->1+5i/2 The answer is 1+5i/2
Let X=3+i---> X-3-i=0
let X=3-i---> X-3+i=0
The quadratic equation : (X-3-i)(x-3+i)=0 multiply the twa factions
X^2-3X+iX-3X+9-3i-iX+3i-i^2=0 Replace i^2 by -1
X^2-6X+9-(-1)=0
X^2-6X+10=0
This is the answer X^2-6X+10=0