(9-2i)(-4+7i)=

Solution for (9-2i)(-4+7i)= equation:

Simplifying
(9 + -2i)(-4 + 7i) = 0

Multiply (9 + -2i) * (-4 + 7i)
(9(-4 + 7i) + -2i * (-4 + 7i)) = 0
((-4 * 9 + 7i * 9) + -2i * (-4 + 7i)) = 0
((-36 + 63i) + -2i * (-4 + 7i)) = 0
(-36 + 63i + (-4 * -2i + 7i * -2i)) = 0
(-36 + 63i + (8i + -14i2)) = 0

Combine like terms: 63i + 8i = 71i
(-36 + 71i + -14i2) = 0

Solving
-36 + 71i + -14i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-9 + 2i)(4 + -7i) = 0

Subproblem 1
Set the factor '(-9 + 2i)' equal to zero and attempt to solve:

Simplifying
-9 + 2i = 0

Solving
-9 + 2i = 0

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

Add '9' to each side of the equation.
-9 + 9 + 2i = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2i = 0 + 9
2i = 0 + 9

Combine like terms: 0 + 9 = 9
2i = 9

Divide each side by '2'.
i = 4.5

Simplifying
i = 4.5
Subproblem 2
Set the factor '(4 + -7i)' equal to zero and attempt to solve:

Simplifying
4 + -7i = 0

Solving
4 + -7i = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7i = 0 + -4
-7i = 0 + -4

Combine like terms: 0 + -4 = -4
-7i = -4

Divide each side by '-7'.
i = 0.5714285714

Simplifying
i = 0.5714285714
Solution
i = {4.5, 0.5714285714}