1-i+i^2=234

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Solution for 1-i+i^2=234 equation:


Simplifying
1 + -1i + i2 = 234

Solving
1 + -1i + i2 = 234

Solving for variable 'i'.

Reorder the terms:
1 + -234 + -1i + i2 = 234 + -234

Combine like terms: 1 + -234 = -233
-233 + -1i + i2 = 234 + -234

Combine like terms: 234 + -234 = 0
-233 + -1i + i2 = 0

Begin completing the square.

Move the constant term to the right:

Add '233' to each side of the equation.
-233 + -1i + 233 + i2 = 0 + 233

Reorder the terms:
-233 + 233 + -1i + i2 = 0 + 233

Combine like terms: -233 + 233 = 0
0 + -1i + i2 = 0 + 233
-1i + i2 = 0 + 233

Combine like terms: 0 + 233 = 233
-1i + i2 = 233

The i term is -1i.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1i + 0.25 + i2 = 233 + 0.25

Reorder the terms:
0.25 + -1i + i2 = 233 + 0.25

Combine like terms: 233 + 0.25 = 233.25
0.25 + -1i + i2 = 233.25

Factor a perfect square on the left side:
(i + -0.5)(i + -0.5) = 233.25

Calculate the square root of the right side: 15.272524349

Break this problem into two subproblems by setting 
(i + -0.5) equal to 15.272524349 and -15.272524349.


Subproblem 1
i + -0.5 = 15.272524349

Simplifying
i + -0.5 = 15.272524349

Reorder the terms:
-0.5 + i = 15.272524349

Solving
-0.5 + i = 15.272524349

Solving for variable 'i'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + i = 15.272524349 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + i = 15.272524349 + 0.5
i = 15.272524349 + 0.5

Combine like terms: 15.272524349 + 0.5 = 15.772524349
i = 15.772524349

Simplifying
i = 15.772524349


Subproblem 2
i + -0.5 = -15.272524349

Simplifying
i + -0.5 = -15.272524349

Reorder the terms:
-0.5 + i = -15.272524349

Solving
-0.5 + i = -15.272524349

Solving for variable 'i'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + i = -15.272524349 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + i = -15.272524349 + 0.5
i = -15.272524349 + 0.5

Combine like terms: -15.272524349 + 0.5 = -14.772524349
i = -14.772524349

Simplifying
i = -14.772524349


Solution
The solution to the problem is based on the solutions
from the subproblems.
i = {15.772524349, -14.772524349}

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