Answer:
a=-11+12i-4iba=−11+12i−4ib
Step-by-step explanation:
Detected Query
4b-5+(-a-3)i=7+8i
4b−5+(−a−3)i=7+8i
Answer
a=-11+12i-4iba=−11+12i−4ib
Step for Solving Equation
Use the distributive property to multiply -a-3−a−3 by ii.
4b-5+i\left(-a\right)-3i=7+8i
4b−5+i(−a)−3i=7+8i
Subtract 4b4b from both sides.
-5+i\left(-a\right)-3i=7+8i-4b
−5+i(−a)−3i=7+8i−4b
Add 55 to both sides.
i\left(-a\right)-3i=7+8i-4b+5
i(−a)−3i=7+8i−4b+5
Do the additions in 7+8i+57+8i+5.
i\left(-a\right)-3i=-4b+12+8i
i(−a)−3i=−4b+12+8i
Add 3i3i to both sides.
i\left(-a\right)=-4b+12+8i+3i
i(−a)=−4b+12+8i+3i
Do the additions in 12+8i+3i12+8i+3i.
i\left(-a\right)=-4b+12+11i
i(−a)=−4b+12+11i
Reorder the terms.
-ia=-4b+12+11i
−ia=−4b+12+11i
The equation is in standard form.
-ia=12+11i-4b
−ia=12+11i−4b
Divide both sides by -i−i.
\frac{-ia}{-i}=\frac{12+11i-4b}{-i}
−i
−ia
=
−i
12+11i−4b
Dividing by -i−i undoes the multiplication by -i−i.
a=\frac{12+11i-4b}{-i}
a=
−i
12+11i−4b
Divide -4b+\left(12+11i\right)−4b+(12+11i) by -i−i.
a=-11+12i-4ib
a=−11+12i−4ib
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-3−a−3 by ii.
4b-5+i\left(-a\right)-3i=7+8i
4b−5+i(−a)−3i=7+8i
Add 55 to both sides.
4b+i\left(-a\right)-3i=7+8i+5
4b+i(−a)−3i=7+8i+5
Add 7+8i7+8i and 55 to get 12+8i12+8i.
4b+i\left(-a\right)-3i=12+8i
4b+i(−a)−3i=12+8i
Subtract i\left(-a\right)i(−a) from both sides.
4b-3i=12+8i-i\left(-a\right)
4b−3i=12+8i−i(−a)
Add 3i3i to both sides.
4b=12+8i-i\left(-a\right)+3i
4b=12+8i−i(−a)+3i
Do the additions in 12+8i+3i12+8i+3i.
4b=-i\left(-1\right)a+12+11i
4b=−i(−1)a+12+11i
Multiply -i−i and -1−1 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\imath4b−5+(−a−3)=7+8
Add 55 to both sides.
4b+\imath (-a-3)=7+8\imath +54b+(−a−3)=7+8+5
Simplify 7+8\imath +57+8+5 to 12+8\imath12+8.
4b+\imath (-a-3)=12+8\imath4b+(−a−3)=12+8
Subtract \imath (-a-3)(−a−3) from both sides.
4b=12+8\imath -\imath (-a-3)4b=12+8−(−a−3)
Divide both sides by 44.
b=\frac{12+8\imath -\imath (-a-3)}{4}b=
4
12+8−(−a−3)
