a=-11+12i-4iba=β11+12iβ4ib
Step-by-step explanation:
Detected Query
4b-5+(-a-3)i=7+8i
4bβ5+(βaβ3)i=7+8i
Answer
a=-11+12i-4iba=β11+12iβ4ib
Step for Solving Equation
Use the distributive property to multiply -a-3βaβ3 by ii.
4b-5+i\left(-a\right)-3i=7+8i
4bβ5+i(βa)β3i=7+8i
Subtract 4b4b from both sides.
-5+i\left(-a\right)-3i=7+8i-4b
β5+i(βa)β3i=7+8iβ4b
Add 55 to both sides.
i\left(-a\right)-3i=7+8i-4b+5
i(βa)β3i=7+8iβ4b+5
Do the additions in 7+8i+57+8i+5.
i\left(-a\right)-3i=-4b+12+8i
i(βa)β3i=β4b+12+8i
Add 3i3i to both sides.
i\left(-a\right)=-4b+12+8i+3i
i(βa)=β4b+12+8i+3i
Do the additions in 12+8i+3i12+8i+3i.
i\left(-a\right)=-4b+12+11i
i(βa)=β4b+12+11i
Reorder the terms.
-ia=-4b+12+11i
βia=β4b+12+11i
The equation is in standard form.
-ia=12+11i-4b
βia=12+11iβ4b
Divide both sides by -iβi.
\frac{-ia}{-i}=\frac{12+11i-4b}{-i}
βi
βia
=
βi
12+11iβ4b
Dividing by -iβi undoes the multiplication by -iβi.
a=\frac{12+11i-4b}{-i}
a=
βi
12+11iβ4b
Divide -4b+\left(12+11i\right)β4b+(12+11i) by -iβi.
a=-11+12i-4ib
a=β11+12iβ4ib
Answer
b=\frac{ia}{4}+\left(3+\frac{11}{4}i\right)b=
4
ia
+(3+
4
11
i)
Step for Solving Equation
Use the distributive property to multiply -a-3βaβ3 by ii.
4b-5+i\left(-a\right)-3i=7+8i
4bβ5+i(βa)β3i=7+8i
Add 55 to both sides.
4b+i\left(-a\right)-3i=7+8i+5
4b+i(βa)β3i=7+8i+5
Add 7+8i7+8i and 55 to get 12+8i12+8i.
4b+i\left(-a\right)-3i=12+8i
4b+i(βa)β3i=12+8i
Subtract i\left(-a\right)i(βa) from both sides.
4b-3i=12+8i-i\left(-a\right)
4bβ3i=12+8iβi(βa)
Add 3i3i to both sides.
4b=12+8i-i\left(-a\right)+3i
4b=12+8iβi(βa)+3i
Do the additions in 12+8i+3i12+8i+3i.
4b=-i\left(-1\right)a+12+11i
4b=βi(β1)a+12+11i
Multiply -iβi and -1β1 to get ii.
4b=ia+12+11i
4b=ia+12+11i
The equation is in standard form.
4b=ia+\left(12+11i\right)
4b=ia+(12+11i)
Divide both sides by 44.
\frac{4b}{4}=\frac{ia+\left(12+11i\right)}{4}
4
4b
=
4
ia+(12+11i)
Dividing by 44 undoes the multiplication by 44.
b=\frac{ia+\left(12+11i\right)}{4}
b=
4
ia+(12+11i)
Divide 12+11i+ia12+11i+ia by 44.
b=\frac{ia}{4}+\left(3+\frac{11}{4}i\right)
b=
4
ia
+(3+
4
11
i)
Solution 2
Solving for b. Want to solve for a instead?
Regroup terms.
4b-5+\imath (-a-3)=7+8\imath4bβ5+ξ±(βaβ3)=7+8ξ±
Add 55 to both sides.
4b+\imath (-a-3)=7+8\imath +54b+ξ±(βaβ3)=7+8ξ±+5
Simplify 7+8\imath +57+8ξ±+5 to 12+8\imath12+8ξ±.
4b+\imath (-a-3)=12+8\imath4b+ξ±(βaβ3)=12+8ξ±
Subtract \imath (-a-3)ξ±(βaβ3) from both sides.
4b=12+8\imath -\imath (-a-3)4b=12+8ξ±βξ±(βaβ3)
Divide both sides by 44.
b=\frac{12+8\imath -\imath (-a-3)}{4}b=
4
12+8ξ±βξ±(βaβ3)