(i-z)(1+2i)+(1-2i)(3-4i)=1+7i

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Solution for (i-z)(1+2i)+(1-2i)(3-4i)=1+7i equation: 


Simplifying
(i + -1z)(1 + 2i) + (1 + -2i)(3 + -4i) = 1 + 7i

Multiply (i + -1z) * (1 + 2i)
(i(1 + 2i) + -1z * (1 + 2i)) + (1 + -2i)(3 + -4i) = 1 + 7i
((1 * i + 2i * i) + -1z * (1 + 2i)) + (1 + -2i)(3 + -4i) = 1 + 7i
((1i + 2i2) + -1z * (1 + 2i)) + (1 + -2i)(3 + -4i) = 1 + 7i
(1i + 2i2 + (1 * -1z + 2i * -1z)) + (1 + -2i)(3 + -4i) = 1 + 7i

Reorder the terms:
(1i + 2i2 + (-2iz + -1z)) + (1 + -2i)(3 + -4i) = 1 + 7i
(1i + 2i2 + (-2iz + -1z)) + (1 + -2i)(3 + -4i) = 1 + 7i

Reorder the terms:
(1i + -2iz + 2i2 + -1z) + (1 + -2i)(3 + -4i) = 1 + 7i
(1i + -2iz + 2i2 + -1z) + (1 + -2i)(3 + -4i) = 1 + 7i

Multiply (1 + -2i) * (3 + -4i)
1i + -2iz + 2i2 + -1z + (1(3 + -4i) + -2i * (3 + -4i)) = 1 + 7i
1i + -2iz + 2i2 + -1z + ((3 * 1 + -4i * 1) + -2i * (3 + -4i)) = 1 + 7i
1i + -2iz + 2i2 + -1z + ((3 + -4i) + -2i * (3 + -4i)) = 1 + 7i
1i + -2iz + 2i2 + -1z + (3 + -4i + (3 * -2i + -4i * -2i)) = 1 + 7i
1i + -2iz + 2i2 + -1z + (3 + -4i + (-6i + 8i2)) = 1 + 7i

Combine like terms: -4i + -6i = -10i
1i + -2iz + 2i2 + -1z + (3 + -10i + 8i2) = 1 + 7i

Reorder the terms:
3 + 1i + -10i + -2iz + 2i2 + 8i2 + -1z = 1 + 7i

Combine like terms: 1i + -10i = -9i
3 + -9i + -2iz + 2i2 + 8i2 + -1z = 1 + 7i

Combine like terms: 2i2 + 8i2 = 10i2
3 + -9i + -2iz + 10i2 + -1z = 1 + 7i

Solving
3 + -9i + -2iz + 10i2 + -1z = 1 + 7i

Solving for variable 'i'.

Reorder the terms:
3 + -1 + -9i + -7i + -2iz + 10i2 + -1z = 1 + 7i + -1 + -7i

Combine like terms: 3 + -1 = 2
2 + -9i + -7i + -2iz + 10i2 + -1z = 1 + 7i + -1 + -7i

Combine like terms: -9i + -7i = -16i
2 + -16i + -2iz + 10i2 + -1z = 1 + 7i + -1 + -7i

Reorder the terms:
2 + -16i + -2iz + 10i2 + -1z = 1 + -1 + 7i + -7i

Combine like terms: 1 + -1 = 0
2 + -16i + -2iz + 10i2 + -1z = 0 + 7i + -7i
2 + -16i + -2iz + 10i2 + -1z = 7i + -7i

Combine like terms: 7i + -7i = 0
2 + -16i + -2iz + 10i2 + -1z = 0

The solution to this equation could not be determined.

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