# Simplify (3/4+4/5*i)-(1/2-3/10*i)

(34+45⋅i)-(12-310⋅i)
Simplify each term.
Combine 45 and i.
34+4i5-(12-310⋅i)
Simplify each term.
Combine i and 310.
34+4i5-(12-i⋅310)
Move 3 to the left of i.
34+4i5-(12-3i10)
34+4i5-(12-3i10)
Apply the distributive property.
34+4i5-12–3i10
Multiply –3i10.
Multiply -1 by -1.
34+4i5-12+13i10
Multiply 3i10 by 1.
34+4i5-12+3i10
34+4i5-12+3i10
34+4i5-12+3i10
To write -12 as a fraction with a common denominator, multiply by 22.
34-12⋅22+4i5+3i10
Write each expression with a common denominator of 4, by multiplying each by an appropriate factor of 1.
Multiply 12 and 22.
34-22⋅2+4i5+3i10
Multiply 2 by 2.
34-24+4i5+3i10
34-24+4i5+3i10
Combine the numerators over the common denominator.
3-24+4i5+3i10
Subtract 2 from 3.
14+4i5+3i10
To write 4i5 as a fraction with a common denominator, multiply by 22.
14+4i5⋅22+3i10
Write each expression with a common denominator of 10, by multiplying each by an appropriate factor of 1.
Multiply 4i5 and 22.
14+4i⋅25⋅2+3i10
Multiply 5 by 2.
14+4i⋅210+3i10
14+4i⋅210+3i10
Combine the numerators over the common denominator.
14+11i10
Simplify (3/4+4/5*i)-(1/2-3/10*i)

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