Solve for a
a=\frac{2+4i}{ib-2}
b\neq -2i
Solve for b
b=-2i+\frac{4-2i}{a}
a\neq 0
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iab+2iai=2+4i
Use the distributive property to multiply ai by b+2i.
iab-2a=2+4i
Multiply 2i and i to get -2.
\left(ib-2\right)a=2+4i
Combine all terms containing a.
\frac{\left(ib-2\right)a}{ib-2}=\frac{2+4i}{ib-2}
Divide both sides by ib-2.
a=\frac{2+4i}{ib-2}
Dividing by ib-2 undoes the multiplication by ib-2.
iab+2iai=2+4i
Use the distributive property to multiply ai by b+2i.
iab-2a=2+4i
Multiply 2i and i to get -2.
iab=2+4i+2a
Add 2a to both sides.
iab=2a+\left(2+4i\right)
The equation is in standard form.
\frac{iab}{ia}=\frac{2a+\left(2+4i\right)}{ia}
Divide both sides by ia.
b=\frac{2a+\left(2+4i\right)}{ia}
Dividing by ia undoes the multiplication by ia.
b=-2i+\frac{4-2i}{a}
Divide 2+4i+2a by ia.
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Limits
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