Solve for y -9x+8i=-54+(16y)i

Math
-9x+8i=-54+(16y)i
Rewrite the equation as -54+(16y)i=-9x+8i.
-54+(16y)i=-9x+8i
Multiply 16y by i.
-54+16yi=-9x+8i
Add 54 to both sides of the equation.
16yi=-9x+8i+54
Divide each term by 16i and simplify.
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Divide each term in 16yi=-9x+8i+54 by 16i.
16yi16i=-9x16i+8i16i+5416i
Simplify 16yi16i.
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Cancel the common factor of 16.
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Cancel the common factor.
16yi16i=-9x16i+8i16i+5416i
Rewrite the expression.
yii=-9x16i+8i16i+5416i
yii=-9x16i+8i16i+5416i
Cancel the common factor of i.
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Cancel the common factor.
yii=-9x16i+8i16i+5416i
Divide y by 1.
y=-9x16i+8i16i+5416i
y=-9x16i+8i16i+5416i
y=-9x16i+8i16i+5416i
Simplify each term.
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Multiply the numerator and denominator of -9x16i by the conjugate of 16i to make the denominator real.
y=-9x16i⋅ii+8i16i+5416i
Multiply.
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Combine.
y=-9xi16ii+8i16i+5416i
Simplify the denominator.
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Add parentheses.
y=-9xi16(ii)+8i16i+5416i
Raise i to the power of 1.
y=-9xi16(i1i)+8i16i+5416i
Raise i to the power of 1.
y=-9xi16(i1i1)+8i16i+5416i
Use the power rule aman=am+n to combine exponents.
y=-9xi16i1+1+8i16i+5416i
Add 1 and 1.
y=-9xi16i2+8i16i+5416i
Rewrite i2 as -1.
y=-9xi16⋅-1+8i16i+5416i
y=-9xi16⋅-1+8i16i+5416i
y=-9xi16⋅-1+8i16i+5416i
Multiply 16 by -1.
y=-9xi-16+8i16i+5416i
Dividing two negative values results in a positive value.
y=(9)xi16+8i16i+5416i
Cancel the common factor of 8 and 16.
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Factor 8 out of 8i.
y=9xi16+8(i)16i+5416i
Cancel the common factors.
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Factor 8 out of 16i.
y=9xi16+8(i)8(2i)+5416i
Cancel the common factor.
y=9xi16+8i8(2i)+5416i
Rewrite the expression.
y=9xi16+i2i+5416i
y=9xi16+i2i+5416i
y=9xi16+i2i+5416i
Cancel the common factor of i.
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Cancel the common factor.
y=9xi16+i2i+5416i
Rewrite the expression.
y=9xi16+12+5416i
y=9xi16+12+5416i
Cancel the common factor of 54 and 16.
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Factor 2 out of 54.
y=9xi16+12+2(27)16i
Cancel the common factors.
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Factor 2 out of 16i.
y=9xi16+12+2(27)2(8i)
Cancel the common factor.
y=9xi16+12+2⋅272(8i)
Rewrite the expression.
y=9xi16+12+278i
y=9xi16+12+278i
y=9xi16+12+278i
Multiply the numerator and denominator of 278i by the conjugate of 8i to make the denominator real.
y=9xi16+12+278i⋅ii
Multiply.
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Combine.
y=9xi16+12+27i8ii
Simplify the denominator.
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Add parentheses.
y=9xi16+12+27i8(ii)
Raise i to the power of 1.
y=9xi16+12+27i8(i1i)
Raise i to the power of 1.
y=9xi16+12+27i8(i1i1)
Use the power rule aman=am+n to combine exponents.
y=9xi16+12+27i8i1+1
Add 1 and 1.
y=9xi16+12+27i8i2
Rewrite i2 as -1.
y=9xi16+12+27i8⋅-1
y=9xi16+12+27i8⋅-1
y=9xi16+12+27i8⋅-1
Multiply 8 by -1.
y=9xi16+12+27i-8
Move the negative in front of the fraction.
y=9xi16+12-27i8
y=9xi16+12-27i8
y=9xi16+12-27i8
Solve for y -9x+8i=-54+(16y)i

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