(1+2i)(2+5i)=

Solution for (1+2i)(2+5i)= equation:

Simplifying
(1 + 2i)(2 + 5i) = 0

Multiply (1 + 2i) * (2 + 5i)
(1(2 + 5i) + 2i * (2 + 5i)) = 0
((2 * 1 + 5i * 1) + 2i * (2 + 5i)) = 0
((2 + 5i) + 2i * (2 + 5i)) = 0
(2 + 5i + (2 * 2i + 5i * 2i)) = 0
(2 + 5i + (4i + 10i2)) = 0

Combine like terms: 5i + 4i = 9i
(2 + 9i + 10i2) = 0

Solving
2 + 9i + 10i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(1 + 2i)(2 + 5i) = 0

Subproblem 1
Set the factor '(1 + 2i)' equal to zero and attempt to solve:

Simplifying
1 + 2i = 0

Solving
1 + 2i = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2i = 0 + -1
2i = 0 + -1

Combine like terms: 0 + -1 = -1
2i = -1

Divide each side by '2'.
i = -0.5

Simplifying
i = -0.5
Subproblem 2
Set the factor '(2 + 5i)' equal to zero and attempt to solve:

Simplifying
2 + 5i = 0

Solving
2 + 5i = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5i = 0 + -2
5i = 0 + -2

Combine like terms: 0 + -2 = -2
5i = -2

Divide each side by '5'.
i = -0.4

Simplifying
i = -0.4
Solution
i = {-0.5, -0.4}