(4i+3j)*(7i+5j)=

Solution for (4i+3j)*(7i+5j)= equation:

Simplifying
(4i + 3j)(7i + 5j) = 0

Multiply (4i + 3j) * (7i + 5j)
(4i * (7i + 5j) + 3j * (7i + 5j)) = 0
((7i * 4i + 5j * 4i) + 3j * (7i + 5j)) = 0

Reorder the terms:
((20ij + 28i2) + 3j * (7i + 5j)) = 0
((20ij + 28i2) + 3j * (7i + 5j)) = 0
(20ij + 28i2 + (7i * 3j + 5j * 3j)) = 0
(20ij + 28i2 + (21ij + 15j2)) = 0

Reorder the terms:
(20ij + 21ij + 28i2 + 15j2) = 0

Combine like terms: 20ij + 21ij = 41ij
(41ij + 28i2 + 15j2) = 0

Solving
41ij + 28i2 + 15j2 = 0

Solving for variable 'i'.

Factor a trinomial.
(7i + 5j)(4i + 3j) = 0

Subproblem 1
Set the factor '(7i + 5j)' equal to zero and attempt to solve:

Simplifying
7i + 5j = 0

Solving
7i + 5j = 0

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

Add '-5j' to each side of the equation.
7i + 5j + -5j = 0 + -5j

Combine like terms: 5j + -5j = 0
7i + 0 = 0 + -5j
7i = 0 + -5j
Remove the zero:
7i = -5j

Divide each side by '7'.
i = -0.7142857143j

Simplifying
i = -0.7142857143j
Subproblem 2
Set the factor '(4i + 3j)' equal to zero and attempt to solve:

Simplifying
4i + 3j = 0

Solving
4i + 3j = 0

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

Add '-3j' to each side of the equation.
4i + 3j + -3j = 0 + -3j

Combine like terms: 3j + -3j = 0
4i + 0 = 0 + -3j
4i = 0 + -3j
Remove the zero:
4i = -3j

Divide each side by '4'.
i = -0.75j

Simplifying
i = -0.75j
Solution
i = {-0.7142857143j, -0.75j}