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

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


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

Multiply (7 + 2i) * (7 + -3i)
(7(7 + -3i) + 2i * (7 + -3i)) = 0
((7 * 7 + -3i * 7) + 2i * (7 + -3i)) = 0
((49 + -21i) + 2i * (7 + -3i)) = 0
(49 + -21i + (7 * 2i + -3i * 2i)) = 0
(49 + -21i + (14i + -6i2)) = 0

Combine like terms: -21i + 14i = -7i
(49 + -7i + -6i2) = 0

Solving
49 + -7i + -6i2 = 0

Solving for variable 'i'.

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


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

Simplifying
7 + -3i = 0

Solving
7 + -3i = 0

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

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

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

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

Divide each side by '-3'.
i = 2.333333333

Simplifying
i = 2.333333333

Subproblem 2
Set the factor '(7 + 2i)' equal to zero and attempt to solve:

Simplifying
7 + 2i = 0

Solving
7 + 2i = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2i = 0 + -7
2i = 0 + -7

Combine like terms: 0 + -7 = -7
2i = -7

Divide each side by '2'.
i = -3.5

Simplifying
i = -3.5
Solution
i = {2.333333333, -3.5}

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