+6251 what is (x+(3+2i)) times (x-(3+2i)) ?
note that
\((a+b)(a-b)=a^2 - b^2\)
and we get
\( (x+(3+2i)) (x-(3+2i))= x^2 -(3+2i)^2\)
\((3+2i)^2 = (9-4)+12i=5+12i\)
\( (x+(3+2i)) (x-(3+2i)) = x^2-5 -12i\)
Solve for x:
(-(12 i)-5)+x^2 = 0
(-(12 i)-5)+x^2 = x^2+(-5-12 i):
x^2+(-5-12 i) = 0
The left hand side factors into a product with two terms:
(x+(-3-2 i)) ((3+2 i)+x) = 0
Split into two equations:
x+(-3-2 i) = 0 or (3+2 i)+x = 0
Add 3+2 i to both sides:
x = 3+2 i or (3+2 i)+x = 0
Subtract 3+2 i from both sides:
Answer: | x = 3+2i or x = -3-2i
