SOLUTION: Please help me solve the following and I would be ever so grateful: 1. Write the quotient in standard form: 2-3i/1-2i 2. Multiply. Write answer in standard form: (7-2i)(3-5i)

Algebra ->  Linear-equations -> SOLUTION: Please help me solve the following and I would be ever so grateful: 1. Write the quotient in standard form: 2-3i/1-2i 2. Multiply. Write answer in standard form: (7-2i)(3-5i)      Log On


   

Question 716606: Please help me solve the following and I would be ever so grateful:
1. Write the quotient in standard form: 2-3i/1-2i
2. Multiply. Write answer in standard form: (7-2i)(3-5i)
3. Solve: (1/2)x^2 + (3/8)x = 2
4. Solve: (x + 3)^3/2 = 8
Thank you so much!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
1. Use parentheses when needed.
Rationalize by multiplying numerator and denominator times the conjugate.
(2-3i)/(1-2i)=

2. FOIL and simplify.
%287-2i%29%283-5i%29=21-35i-6i%2B10i%5E2=21-41i-10=11-41i

3. Eliminate denominator by multiplying both sides of the equal sign times 8.
%281%2F2%29x%5E2+%2B+%283%2F8%29x+=+2 --> 4x%5E2+%2B+3x+=+16 --> 4x%5E2+%2B+3x+-+16=0
Now, just apply the quadratic formula
x+=+%28-3+%2B-+sqrt%283%5E2-4%2A4%2A%28-16%29%29%29%2F%282%2A4%29+
x+=+%28-3+%2B-+sqrt%289%2B256%29%29%2F8+
highlight%28x+=+%28-3+%2B-+sqrt%28365%29%29%2F8%29

4. (x + 3)^(3/2) = 8 unfortunately shows as %28x+%2B+3%29%5E%283%2F2%29
with the top of the exponent chopped off (at least on my screen), so I'll improvise
(x + 3)^(3/2) = 8 --> (x + 3)^(3/2) = 2%5E3
Square both sides
%28%28x+%2B+3%29%5E%283%2F2%29%29%5E2+=+%282%5E3%29%5E2 --> %28x+%2B+3%29%5E3+=+2%5E6 --> %28x+%2B+3%29%5E3+=+%282%5E2%29%5E3} --> %28x+%2B+3%29%5E3+=+4%5E3
I could say take cubic roots on both sides to get
x%2B3=4 --> highlight%28x=1%29