(-5i)(1-4i)+6(-3-i)=

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Solution for (-5i)(1-4i)+6(-3-i)= equation:


Simplifying
(-5i)(1 + -4i) + 6(-3 + -1i) = 0

Remove parenthesis around (-5i)
-5i(1 + -4i) + 6(-3 + -1i) = 0
(1 * -5i + -4i * -5i) + 6(-3 + -1i) = 0
(-5i + 20i2) + 6(-3 + -1i) = 0
-5i + 20i2 + (-3 * 6 + -1i * 6) = 0
-5i + 20i2 + (-18 + -6i) = 0

Reorder the terms:
-18 + -5i + -6i + 20i2 = 0

Combine like terms: -5i + -6i = -11i
-18 + -11i + 20i2 = 0

Solving
-18 + -11i + 20i2 = 0

Solving for variable 'i'.

Begin completing the square.  Divide all terms by
20 the coefficient of the squared term: 

Divide each side by '20'.
-0.9 + -0.55i + i2 = 0.0

Move the constant term to the right:

Add '0.9' to each side of the equation.
-0.9 + -0.55i + 0.9 + i2 = 0.0 + 0.9

Reorder the terms:
-0.9 + 0.9 + -0.55i + i2 = 0.0 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + -0.55i + i2 = 0.0 + 0.9
-0.55i + i2 = 0.0 + 0.9

Combine like terms: 0.0 + 0.9 = 0.9
-0.55i + i2 = 0.9

The i term is -0.55i.  Take half its coefficient (-0.275).
Square it (0.075625) and add it to both sides.

Add '0.075625' to each side of the equation.
-0.55i + 0.075625 + i2 = 0.9 + 0.075625

Reorder the terms:
0.075625 + -0.55i + i2 = 0.9 + 0.075625

Combine like terms: 0.9 + 0.075625 = 0.975625
0.075625 + -0.55i + i2 = 0.975625

Factor a perfect square on the left side:
(i + -0.275)(i + -0.275) = 0.975625

Calculate the square root of the right side: 0.987737313

Break this problem into two subproblems by setting 
(i + -0.275) equal to 0.987737313 and -0.987737313.

Subproblem 1

i + -0.275 = 0.987737313 Simplifying i + -0.275 = 0.987737313 Reorder the terms: -0.275 + i = 0.987737313 Solving -0.275 + i = 0.987737313 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + i = 0.987737313 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + i = 0.987737313 + 0.275 i = 0.987737313 + 0.275 Combine like terms: 0.987737313 + 0.275 = 1.262737313 i = 1.262737313 Simplifying i = 1.262737313

Subproblem 2

i + -0.275 = -0.987737313 Simplifying i + -0.275 = -0.987737313 Reorder the terms: -0.275 + i = -0.987737313 Solving -0.275 + i = -0.987737313 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + i = -0.987737313 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + i = -0.987737313 + 0.275 i = -0.987737313 + 0.275 Combine like terms: -0.987737313 + 0.275 = -0.712737313 i = -0.712737313 Simplifying i = -0.712737313

Solution

The solution to the problem is based on the solutions from the subproblems. i = {1.262737313, -0.712737313}

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