SOLUTION: 1. 1 + i divided by 3 - 2i = 2. x{2} - 3 = 0 3. 4 divided by 5 - i = 4. x{2} + 2x + 5 = 0 5. -2x{2} + 3x = 3 = 0 6. x{2} + 3x - 2 = 0

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: 1. 1 + i divided by 3 - 2i = 2. x{2} - 3 = 0 3. 4 divided by 5 - i = 4. x{2} + 2x + 5 = 0 5. -2x{2} + 3x = 3 = 0 6. x{2} + 3x - 2 = 0      Log On


   

Question 126363: 1. 1 + i divided by 3 - 2i =
2. x{2} - 3 = 0
3. 4 divided by 5 - i =
4. x{2} + 2x + 5 = 0
5. -2x{2} + 3x = 3 = 0
6. x{2} + 3x - 2 = 0
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You have 2 problems with complex number division and 4 quadratic equations. I'll do one of each:

#1: To do complex number division, multiply both numerator and denominator by the conjugate of the complex number. The conjugate is formed by changing the sign on the imaginary term.

%281%2Bi%29%2F%283-2i%29. The conjugate of 3-2i is 3%2B2i, so:

%28%281%2Bi%29%283%2B2i%29%29%2F%28%283-2i%29%283%2B2i%29%29.

Use FOIL on the numerator and the factorization of the difference of two squares on the denominator, simplify the expression. Remember that i%5E2=-1,

%283%2B2i%2B3i-2%29%2F%289%2B4%29

%281%2B5i%29%2F13. Done.

#4. x%5E2%2B2x%2B5=0

Use the quadradic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29+

x+=+%28-2+%2B-+sqrt%28+4-20+%29%29%2F%282%29+

x+=+%28-2+%2B-+sqrt%28+-16+%29%29%2F%282%29+

x%5B1%5D=-1%2B2i, x%5B2%5D=-1-2i