(3+i)(3-i)=

Solution for (3+i)(3-i)= equation:

Simplifying
(3 + i)(3 + -1i) = 0

Multiply (3 + i) * (3 + -1i)
(3(3 + -1i) + i(3 + -1i)) = 0
((3 * 3 + -1i * 3) + i(3 + -1i)) = 0
((9 + -3i) + i(3 + -1i)) = 0
(9 + -3i + (3 * i + -1i * i)) = 0
(9 + -3i + (3i + -1i2)) = 0

Combine like terms: -3i + 3i = 0
(9 + 0 + -1i2) = 0
(9 + -1i2) = 0

Solving
9 + -1i2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -1i2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1i2 = 0 + -9
-1i2 = 0 + -9

Combine like terms: 0 + -9 = -9
-1i2 = -9

Divide each side by '-1'.
i2 = 9

Simplifying
i2 = 9

Take the square root of each side:
i = {-3, 3}