# Rewrite in Standard Form (1+i)/(2-i)

1+i2-i
Multiply the numerator and denominator of 1+i2-i by the conjugate of 2-i to make the denominator real.
1+i2-i⋅2+i2+i
Multiply.
Combine.
(1+i)(2+i)(2-i)(2+i)
Simplify the numerator.
Expand (1+i)(2+i) using the FOIL Method.
Apply the distributive property.
1(2+i)+i(2+i)(2-i)(2+i)
Apply the distributive property.
1⋅2+1i+i(2+i)(2-i)(2+i)
Apply the distributive property.
1⋅2+1i+i⋅2+ii(2-i)(2+i)
1⋅2+1i+i⋅2+ii(2-i)(2+i)
Simplify and combine like terms.
Simplify each term.
Multiply 2 by 1.
2+1i+i⋅2+ii(2-i)(2+i)
Multiply i by 1.
2+i+i⋅2+ii(2-i)(2+i)
Move 2 to the left of i.
2+i+2⋅i+ii(2-i)(2+i)
Multiply ii.
Raise i to the power of 1.
2+i+2i+i1i(2-i)(2+i)
Raise i to the power of 1.
2+i+2i+i1i1(2-i)(2+i)
Use the power rule aman=am+n to combine exponents.
2+i+2i+i1+1(2-i)(2+i)
2+i+2i+i2(2-i)(2+i)
2+i+2i+i2(2-i)(2+i)
Rewrite i2 as -1.
2+i+2i-1(2-i)(2+i)
2+i+2i-1(2-i)(2+i)
Subtract 1 from 2.
1+i+2i(2-i)(2+i)
1+3i(2-i)(2+i)
1+3i(2-i)(2+i)
1+3i(2-i)(2+i)
Simplify the denominator.
Expand (2-i)(2+i) using the FOIL Method.
Apply the distributive property.
1+3i2(2+i)-i(2+i)
Apply the distributive property.
1+3i2⋅2+2i-i(2+i)
Apply the distributive property.
1+3i2⋅2+2i-i⋅2-ii
1+3i2⋅2+2i-i⋅2-ii
Simplify.
Multiply 2 by 2.
1+3i4+2i-i⋅2-ii
Multiply 2 by -1.
1+3i4+2i-2i-ii
Raise i to the power of 1.
1+3i4+2i-2i-(i1i)
Raise i to the power of 1.
1+3i4+2i-2i-(i1i1)
Use the power rule aman=am+n to combine exponents.
1+3i4+2i-2i-i1+1
1+3i4+2i-2i-i2
Subtract 2i from 2i.
1+3i4+0-i2
1+3i4-i2
1+3i4-i2
Simplify each term.
Rewrite i2 as -1.
1+3i4–1
Multiply -1 by -1.
1+3i4+1
1+3i4+1