1.21=(1+i)(1+i)

Solution for 1.21=(1+i)(1+i) equation:

Simplifying
1.21 = (1 + i)(1 + i)

Multiply (1 + i) * (1 + i)
1.21 = (1(1 + i) + i(1 + i))
1.21 = ((1 * 1 + i * 1) + i(1 + i))
1.21 = ((1 + 1i) + i(1 + i))
1.21 = (1 + 1i + (1 * i + i * i))
1.21 = (1 + 1i + (1i + i2))

Combine like terms: 1i + 1i = 2i
1.21 = (1 + 2i + i2)

Solving
1.21 = 1 + 2i + i2

Solving for variable 'i'.

Combine like terms: 1.21 + -1 = 0.21
0.21 + -2i + -1i2 = 1 + 2i + i2 + -1 + -2i + -1i2

Reorder the terms:
0.21 + -2i + -1i2 = 1 + -1 + 2i + -2i + i2 + -1i2

Combine like terms: 1 + -1 = 0
0.21 + -2i + -1i2 = 0 + 2i + -2i + i2 + -1i2
0.21 + -2i + -1i2 = 2i + -2i + i2 + -1i2

Combine like terms: 2i + -2i = 0
0.21 + -2i + -1i2 = 0 + i2 + -1i2
0.21 + -2i + -1i2 = i2 + -1i2

Combine like terms: i2 + -1i2 = 0
0.21 + -2i + -1i2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.21 + 2i + i2 = 0

Move the constant term to the right:

Add '0.21' to each side of the equation.
-0.21 + 2i + 0.21 + i2 = 0 + 0.21

Reorder the terms:
-0.21 + 0.21 + 2i + i2 = 0 + 0.21

Combine like terms: -0.21 + 0.21 = 0.00
0.00 + 2i + i2 = 0 + 0.21
2i + i2 = 0 + 0.21

Combine like terms: 0 + 0.21 = 0.21
2i + i2 = 0.21

The i term is 2i.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2i + 1 + i2 = 0.21 + 1

Reorder the terms:
1 + 2i + i2 = 0.21 + 1

Combine like terms: 0.21 + 1 = 1.21
1 + 2i + i2 = 1.21

Factor a perfect square on the left side:
(i + 1)(i + 1) = 1.21

Calculate the square root of the right side: 1.1

Break this problem into two subproblems by setting 
(i + 1) equal to 1.1 and -1.1.

Subproblem 1
i + 1 = 1.1

Simplifying
i + 1 = 1.1

Reorder the terms:
1 + i = 1.1

Solving
1 + i = 1.1

Solving for variable 'i'.

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

Add '-1' to each side of the equation.
1 + -1 + i = 1.1 + -1

Combine like terms: 1 + -1 = 0
0 + i = 1.1 + -1
i = 1.1 + -1

Combine like terms: 1.1 + -1 = 0.1
i = 0.1

Simplifying
i = 0.1

Subproblem 2
i + 1 = -1.1

Simplifying
i + 1 = -1.1

Reorder the terms:
1 + i = -1.1

Solving
1 + i = -1.1

Solving for variable 'i'.

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

Add '-1' to each side of the equation.
1 + -1 + i = -1.1 + -1

Combine like terms: 1 + -1 = 0
0 + i = -1.1 + -1
i = -1.1 + -1

Combine like terms: -1.1 + -1 = -2.1
i = -2.1

Simplifying
i = -2.1

Solution
The solution to the problem is based on the solutions
from the subproblems.
i = {0.1, -2.1}