3⋅(12yi)=27+36i

Multiply 12 by 3.

36⋅(yi)=27+36i

Divide each term in 36⋅(yi)=27+36i by 36i.

36⋅(yi)36i=2736i+36i36i

Simplify 36⋅(yi)36i.

Cancel the common factor of 36.

Cancel the common factor.

36⋅(yi)36i=2736i+36i36i

Rewrite the expression.

yii=2736i+36i36i

yii=2736i+36i36i

Cancel the common factor of i.

Cancel the common factor.

yii=2736i+36i36i

Divide y by 1.

y=2736i+36i36i

y=2736i+36i36i

y=2736i+36i36i

Simplify 2736i+36i36i.

Simplify each term.

Cancel the common factor of 27 and 36.

Factor 9 out of 27.

y=9(3)36i+36i36i

Cancel the common factors.

Factor 9 out of 36i.

y=9(3)9(4i)+36i36i

Cancel the common factor.

y=9⋅39(4i)+36i36i

Rewrite the expression.

y=34i+36i36i

y=34i+36i36i

y=34i+36i36i

Multiply the numerator and denominator of 34i by the conjugate of 4i to make the denominator real.

y=34i⋅ii+36i36i

Multiply.

Combine.

y=3i4ii+36i36i

Simplify the denominator.

Add parentheses.

y=3i4(ii)+36i36i

Raise i to the power of 1.

y=3i4(i1i)+36i36i

Raise i to the power of 1.

y=3i4(i1i1)+36i36i

Use the power rule aman=am+n to combine exponents.

y=3i4i1+1+36i36i

Add 1 and 1.

y=3i4i2+36i36i

Rewrite i2 as -1.

y=3i4⋅-1+36i36i

y=3i4⋅-1+36i36i

y=3i4⋅-1+36i36i

Multiply 4 by -1.

y=3i-4+36i36i

Move the negative in front of the fraction.

y=-3i4+36i36i

Cancel the common factor of 36.

Cancel the common factor.

y=-3i4+36i36i

Rewrite the expression.

y=-3i4+ii

y=-3i4+ii

Cancel the common factor of i.

Cancel the common factor.

y=-3i4+ii

Divide 1 by 1.

y=-3i4+1

y=-3i4+1

y=-3i4+1

Reorder -3i4 and 1.

y=1-3i4

y=1-3i4

y=1-3i4

Solve for y 3*(12yi)=27+36i