Answer:
Simplifying
4b + -5 + (-1a + -3) * i = 7 + -8i
Reorder the terms:
4b + -5 + (-3 + -1a) * i = 7 + -8i
Reorder the terms for easier multiplication:
4b + -5 + i(-3 + -1a) = 7 + -8i
4b + -5 + (-3 * i + -1a * i) = 7 + -8i
Reorder the terms:
4b + -5 + (-1ai + -3i) = 7 + -8i
4b + -5 + (-1ai + -3i) = 7 + -8i
Reorder the terms:
-5 + -1ai + 4b + -3i = 7 + -8i
Solving
-5 + -1ai + 4b + -3i = 7 + -8i
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + -1ai + 4b + 5 + -3i = 7 + 5 + -8i
Reorder the terms:
-5 + 5 + -1ai + 4b + -3i = 7 + 5 + -8i
Combine like terms: -5 + 5 = 0
0 + -1ai + 4b + -3i = 7 + 5 + -8i
-1ai + 4b + -3i = 7 + 5 + -8i
Combine like terms: 7 + 5 = 12
-1ai + 4b + -3i = 12 + -8i
Add '-4b' to each side of the equation.
-1ai + 4b + -4b + -3i = 12 + -4b + -8i
Combine like terms: 4b + -4b = 0
-1ai + 0 + -3i = 12 + -4b + -8i
-1ai + -3i = 12 + -4b + -8i
Add '3i' to each side of the equation.
-1ai + -3i + 3i = 12 + -4b + -8i + 3i
Combine like terms: -3i + 3i = 0
-1ai + 0 = 12 + -4b + -8i + 3i
-1ai = 12 + -4b + -8i + 3i
Combine like terms: -8i + 3i = -5i
-1ai = 12 + -4b + -5i
Divide each side by '-1i'.
a = -12i-1 + 4bi-1 + 5
Simplifying
a = -12i-1 + 4bi-1 + 5
Reorder the terms:
a = 5 + 4bi-1 + -12i-1
![\begin{tabular} {|c|c|} Statement&Reason\\[1ex] Line m is parallel to line n&Given\\ \angle1\cong\angle2&Corresponding angles\\ m\angle1=m\angle2&Deifinition of Congruent angles\\ \angle2\ and\ \angle3\ form\ a\ linear\ pair&Adjacent angles on a straight line\\ \angle2\ is\ supplementary\ to\ \angle3&Deifinition of linear pair\\ m\angle2+m\angle3=180^o&Deifinition of supplementary \angle s\\ m\angle1+m\angle3=180^o&Substitution Property \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7C%7D%0AStatement%26Reason%5C%5C%5B1ex%5D%0ALine%20m%20is%20parallel%20to%20line%20n%26Given%5C%5C%0A%5Cangle1%5Ccong%5Cangle2%26Corresponding%20angles%5C%5C%0Am%5Cangle1%3Dm%5Cangle2%26Deifinition%20of%20Congruent%20angles%5C%5C%0A%5Cangle2%5C%20and%5C%20%5Cangle3%5C%20form%5C%20a%5C%20linear%5C%20pair%26Adjacent%20angles%20on%20a%20straight%20line%5C%5C%0A%5Cangle2%5C%20is%5C%20supplementary%5C%20to%5C%20%5Cangle3%26Deifinition%20of%20linear%20pair%5C%5C%0Am%5Cangle2%2Bm%5Cangle3%3D180%5Eo%26Deifinition%20of%20supplementary%20%5Cangle%20s%5C%5C%0Am%5Cangle1%2Bm%5Cangle3%3D180%5Eo%26Substitution%20Property%0A%5Cend%7Btabular%7D)
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