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\left(-2+2i\right)b
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\left(-2+2i\right)b
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a-b+ia+ib-\left(a+b+\left(a-b\right)i\right)
Use the distributive property to multiply a+b by i.
\left(1+i\right)a-b+ib-\left(a+b+\left(a-b\right)i\right)
Combine a and ia to get \left(1+i\right)a.
\left(1+i\right)a+\left(-1+i\right)b-\left(a+b+\left(a-b\right)i\right)
Combine -b and ib to get \left(-1+i\right)b.
\left(1+i\right)a+\left(-1+i\right)b-\left(a+b+ia-ib\right)
Use the distributive property to multiply a-b by i.
\left(1+i\right)a+\left(-1+i\right)b-\left(\left(1+i\right)a+b-ib\right)
Combine a and ia to get \left(1+i\right)a.
\left(1+i\right)a+\left(-1+i\right)b-\left(\left(1+i\right)a+\left(1-i\right)b\right)
Combine b and -ib to get \left(1-i\right)b.
\left(1+i\right)a+\left(-1+i\right)b+\left(-1-i\right)a+\left(-1+i\right)b
To find the opposite of \left(1+i\right)a+\left(1-i\right)b, find the opposite of each term.
\left(-1+i\right)b+\left(-1+i\right)b
Combine \left(1+i\right)a and \left(-1-i\right)a to get 0.
\left(-2+2i\right)b
Combine \left(-1+i\right)b and \left(-1+i\right)b to get \left(-2+2i\right)b.
a-b+ia+ib-\left(a+b+\left(a-b\right)i\right)
Use the distributive property to multiply a+b by i.
\left(1+i\right)a-b+ib-\left(a+b+\left(a-b\right)i\right)
Combine a and ia to get \left(1+i\right)a.
\left(1+i\right)a+\left(-1+i\right)b-\left(a+b+\left(a-b\right)i\right)
Combine -b and ib to get \left(-1+i\right)b.
\left(1+i\right)a+\left(-1+i\right)b-\left(a+b+ia-ib\right)
Use the distributive property to multiply a-b by i.
\left(1+i\right)a+\left(-1+i\right)b-\left(\left(1+i\right)a+b-ib\right)
Combine a and ia to get \left(1+i\right)a.
\left(1+i\right)a+\left(-1+i\right)b-\left(\left(1+i\right)a+\left(1-i\right)b\right)
Combine b and -ib to get \left(1-i\right)b.
\left(1+i\right)a+\left(-1+i\right)b+\left(-1-i\right)a+\left(-1+i\right)b
To find the opposite of \left(1+i\right)a+\left(1-i\right)b, find the opposite of each term.
\left(-1+i\right)b+\left(-1+i\right)b
Combine \left(1+i\right)a and \left(-1-i\right)a to get 0.
\left(-2+2i\right)b
Combine \left(-1+i\right)b and \left(-1+i\right)b to get \left(-2+2i\right)b.
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