(5+2i)(5-2i)=0

Solution for (5+2i)(5-2i)=0 equation:

Simplifying
(5 + 2i)(5 + -2i) = 0

Multiply (5 + 2i) * (5 + -2i)
(5(5 + -2i) + 2i * (5 + -2i)) = 0
((5 * 5 + -2i * 5) + 2i * (5 + -2i)) = 0
((25 + -10i) + 2i * (5 + -2i)) = 0
(25 + -10i + (5 * 2i + -2i * 2i)) = 0
(25 + -10i + (10i + -4i2)) = 0

Combine like terms: -10i + 10i = 0
(25 + 0 + -4i2) = 0
(25 + -4i2) = 0

Solving
25 + -4i2 = 0

Solving for variable 'i'.

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

Add '-25' to each side of the equation.
25 + -25 + -4i2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -4i2 = 0 + -25
-4i2 = 0 + -25

Combine like terms: 0 + -25 = -25
-4i2 = -25

Divide each side by '-4'.
i2 = 6.25

Simplifying
i2 = 6.25

Take the square root of each side:
i = {-2.5, 2.5}