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
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