4b - 5 + (-a-3) i = 7 * 8i

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

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)

m a t h w a y. c o m

step-by-step explanation: