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

Solution for (1-4i)(1+4i)= equation:

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

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

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

Solving
1 + -16i2 = 0

Solving for variable 'i'.

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

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

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

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

Divide each side by '-16'.
i2 = 0.0625

Simplifying
i2 = 0.0625

Take the square root of each side:
i = {-0.25, 0.25}