(-1+2i)(-3+7i)=0

Solution for (-1+2i)(-3+7i)=0 equation:

Simplifying
(-1 + 2i)(-3 + 7i) = 0

Multiply (-1 + 2i) * (-3 + 7i)
(-1(-3 + 7i) + 2i * (-3 + 7i)) = 0
((-3 * -1 + 7i * -1) + 2i * (-3 + 7i)) = 0
((3 + -7i) + 2i * (-3 + 7i)) = 0
(3 + -7i + (-3 * 2i + 7i * 2i)) = 0
(3 + -7i + (-6i + 14i2)) = 0

Combine like terms: -7i + -6i = -13i
(3 + -13i + 14i2) = 0

Solving
3 + -13i + 14i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + -7i)(1 + -2i) = 0

Subproblem 1
Set the factor '(3 + -7i)' equal to zero and attempt to solve:

Simplifying
3 + -7i = 0

Solving
3 + -7i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -7i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7i = 0 + -3
-7i = 0 + -3

Combine like terms: 0 + -3 = -3
-7i = -3

Divide each side by '-7'.
i = 0.4285714286

Simplifying
i = 0.4285714286
Subproblem 2
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
Solution
i = {0.4285714286, 0.5}