(3+5i)(-3-i)=0

Solution for (3+5i)(-3-i)=0 equation:

Simplifying
(3 + 5i)(-3 + -1i) = 0

Multiply (3 + 5i) * (-3 + -1i)
(3(-3 + -1i) + 5i * (-3 + -1i)) = 0
((-3 * 3 + -1i * 3) + 5i * (-3 + -1i)) = 0
((-9 + -3i) + 5i * (-3 + -1i)) = 0
(-9 + -3i + (-3 * 5i + -1i * 5i)) = 0
(-9 + -3i + (-15i + -5i2)) = 0

Combine like terms: -3i + -15i = -18i
(-9 + -18i + -5i2) = 0

Solving
-9 + -18i + -5i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 18i + 5i2) = 0

Factor a trinomial.
-1((3 + i)(3 + 5i)) = 0

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

Simplifying
3 + i = 0

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

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

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

Simplifying
i = -3
Subproblem 2
Set the factor '(3 + 5i)' equal to zero and attempt to solve:

Simplifying
3 + 5i = 0

Solving
3 + 5i = 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 + 5i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5i = 0 + -3
5i = 0 + -3

Combine like terms: 0 + -3 = -3
5i = -3

Divide each side by '5'.
i = -0.6

Simplifying
i = -0.6
Solution
i = {-3, -0.6}