(a+i)(a+i)(a+i)=18+26i

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Solution for (a+i)(a+i)(a+i)=18+26i equation: 


Simplifying
(a + i)(a + i)(a + i) = 18 + 26i

Multiply (a + i) * (a + i)
(a(a + i) + i(a + i))(a + i) = 18 + 26i
((a * a + i * a) + i(a + i))(a + i) = 18 + 26i

Reorder the terms:
((ai + a2) + i(a + i))(a + i) = 18 + 26i
((ai + a2) + i(a + i))(a + i) = 18 + 26i
(ai + a2 + (a * i + i * i))(a + i) = 18 + 26i
(ai + a2 + (ai + i2))(a + i) = 18 + 26i

Reorder the terms:
(ai + ai + a2 + i2)(a + i) = 18 + 26i

Combine like terms: ai + ai = 2ai
(2ai + a2 + i2)(a + i) = 18 + 26i

Multiply (2ai + a2 + i2) * (a + i)
(2ai * (a + i) + a2(a + i) + i2(a + i)) = 18 + 26i
((a * 2ai + i * 2ai) + a2(a + i) + i2(a + i)) = 18 + 26i

Reorder the terms:
((2ai2 + 2a2i) + a2(a + i) + i2(a + i)) = 18 + 26i
((2ai2 + 2a2i) + a2(a + i) + i2(a + i)) = 18 + 26i
(2ai2 + 2a2i + (a * a2 + i * a2) + i2(a + i)) = 18 + 26i

Reorder the terms:
(2ai2 + 2a2i + (a2i + a3) + i2(a + i)) = 18 + 26i
(2ai2 + 2a2i + (a2i + a3) + i2(a + i)) = 18 + 26i
(2ai2 + 2a2i + a2i + a3 + (a * i2 + i * i2)) = 18 + 26i
(2ai2 + 2a2i + a2i + a3 + (ai2 + i3)) = 18 + 26i

Reorder the terms:
(2ai2 + ai2 + 2a2i + a2i + a3 + i3) = 18 + 26i

Combine like terms: 2ai2 + ai2 = 3ai2
(3ai2 + 2a2i + a2i + a3 + i3) = 18 + 26i

Combine like terms: 2a2i + a2i = 3a2i
(3ai2 + 3a2i + a3 + i3) = 18 + 26i

Solving
3ai2 + 3a2i + a3 + i3 = 18 + 26i

Solving for variable 'a'.

Reorder the terms:
-18 + 3ai2 + 3a2i + a3 + -26i + i3 = 18 + 26i + -18 + -26i

Reorder the terms:
-18 + 3ai2 + 3a2i + a3 + -26i + i3 = 18 + -18 + 26i + -26i

Combine like terms: 18 + -18 = 0
-18 + 3ai2 + 3a2i + a3 + -26i + i3 = 0 + 26i + -26i
-18 + 3ai2 + 3a2i + a3 + -26i + i3 = 26i + -26i

Combine like terms: 26i + -26i = 0
-18 + 3ai2 + 3a2i + a3 + -26i + i3 = 0

The solution to this equation could not be determined.

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