Imaginary algebra problem - help!?

1 ⤊

Imaginary algebra problem - help!?

If the solution to an equation is imaginary or irrational, it takes a bit more effort to check. Replace x by each given number to verify each statement.

Both 2 + 3i and 2 - 3i satisfy x^2-4x+13=0

2007-10-21 05:00:36 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

2 answers

(2+3i)² = -5 + 12i
-4(2+3i) = -8 -12 i
13 = 13
Sum = 0.
Similarly,
(2-3i)² = -5 - 12i
-4(2-3i) = -8 + 12i
13 = 13
Sum = 0
So both numbers satisfy the equation.

2007-10-21 05:33:24 · answer #1 · answered by steiner1745 7 · 0⤊ 0⤋

(2 + 3i)Â² - 4(2 + 3i) + 13
4 + 12i - 9 - 8 - 12i + 13
17 - 17
0

(2 - 3i)Â² - 4(2 - 3i) + 13
4 - 12i - 9 - 8 + 12i + 13
17 - 17
0

2007-10-21 07:02:13 · answer #2 · answered by Como 7 · 1⤊ 0⤋