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

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

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

Multiply (-3 + 7i) * (1 + -3i)
(-3(1 + -3i) + 7i * (1 + -3i)) = 0
((1 * -3 + -3i * -3) + 7i * (1 + -3i)) = 0
((-3 + 9i) + 7i * (1 + -3i)) = 0
(-3 + 9i + (1 * 7i + -3i * 7i)) = 0
(-3 + 9i + (7i + -21i2)) = 0

Combine like terms: 9i + 7i = 16i
(-3 + 16i + -21i2) = 0

Solving
-3 + 16i + -21i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-3 + 7i)(1 + -3i) = 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 + -3i)' equal to zero and attempt to solve:

Simplifying
1 + -3i = 0

Solving
1 + -3i = 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 + -3i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3i = 0 + -1
-3i = 0 + -1

Combine like terms: 0 + -1 = -1
-3i = -1

Divide each side by '-3'.
i = 0.3333333333

Simplifying
i = 0.3333333333
Solution
i = {0.4285714286, 0.3333333333}