(3+4i)*(2-5i)=7

Solution for (3+4i)*(2-5i)=7 equation:

Simplifying
(3 + 4i)(2 + -5i) = 7

Multiply (3 + 4i) * (2 + -5i)
(3(2 + -5i) + 4i * (2 + -5i)) = 7
((2 * 3 + -5i * 3) + 4i * (2 + -5i)) = 7
((6 + -15i) + 4i * (2 + -5i)) = 7
(6 + -15i + (2 * 4i + -5i * 4i)) = 7
(6 + -15i + (8i + -20i2)) = 7

Combine like terms: -15i + 8i = -7i
(6 + -7i + -20i2) = 7

Solving
6 + -7i + -20i2 = 7

Solving for variable 'i'.

Reorder the terms:
6 + -7 + -7i + -20i2 = 7 + -7

Combine like terms: 6 + -7 = -1
-1 + -7i + -20i2 = 7 + -7

Combine like terms: 7 + -7 = 0
-1 + -7i + -20i2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 7i + 20i2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 7i + 20i2)' equal to zero and attempt to solve:

Simplifying
1 + 7i + 20i2 = 0

Solving
1 + 7i + 20i2 = 0

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

Divide each side by '20'.
0.05 + 0.35i + i2 = 0.0

Move the constant term to the right:

Add '-0.05' to each side of the equation.
0.05 + 0.35i + -0.05 + i2 = 0.0 + -0.05

Reorder the terms:
0.05 + -0.05 + 0.35i + i2 = 0.0 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + 0.35i + i2 = 0.0 + -0.05
0.35i + i2 = 0.0 + -0.05

Combine like terms: 0.0 + -0.05 = -0.05
0.35i + i2 = -0.05

The i term is 0.35i.  Take half its coefficient (0.175).
Square it (0.030625) and add it to both sides.

Add '0.030625' to each side of the equation.
0.35i + 0.030625 + i2 = -0.05 + 0.030625

Reorder the terms:
0.030625 + 0.35i + i2 = -0.05 + 0.030625

Combine like terms: -0.05 + 0.030625 = -0.019375
0.030625 + 0.35i + i2 = -0.019375

Factor a perfect square on the left side:
(i + 0.175)(i + 0.175) = -0.019375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.