(4-i)(4+i)=0

Solution for (4-i)(4+i)=0 equation:

Simplifying
(4 + -1i)(4 + i) = 0

Multiply (4 + -1i) * (4 + i)
(4(4 + i) + -1i * (4 + i)) = 0
((4 * 4 + i * 4) + -1i * (4 + i)) = 0
((16 + 4i) + -1i * (4 + i)) = 0
(16 + 4i + (4 * -1i + i * -1i)) = 0
(16 + 4i + (-4i + -1i2)) = 0

Combine like terms: 4i + -4i = 0
(16 + 0 + -1i2) = 0
(16 + -1i2) = 0

Solving
16 + -1i2 = 0

Solving for variable 'i'.

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

Add '-16' to each side of the equation.
16 + -16 + -1i2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1i2 = 0 + -16
-1i2 = 0 + -16

Combine like terms: 0 + -16 = -16
-1i2 = -16

Divide each side by '-1'.
i2 = 16

Simplifying
i2 = 16

Take the square root of each side:
i = {-4, 4}