# Write in Standard Form ((3-i)(1-4i))/(2-i)

(3-i)(1-4i)2-i
Multiply the numerator and denominator of (3-i)(1-4i)2-i by the conjugate of 2-i to make the denominator real.
(3-i)(1-4i)2-i⋅2+i2+i
Multiply.
Combine.
(3-i)(1-4i)(2+i)(2-i)(2+i)
Simplify the numerator.
Expand (3-i)(1-4i) using the FOIL Method.
Apply the distributive property.
(3(1-4i)-i(1-4i))(2+i)(2-i)(2+i)
Apply the distributive property.
(3⋅1+3(-4i)-i(1-4i))(2+i)(2-i)(2+i)
Apply the distributive property.
(3⋅1+3(-4i)-i⋅1-i(-4i))(2+i)(2-i)(2+i)
(3⋅1+3(-4i)-i⋅1-i(-4i))(2+i)(2-i)(2+i)
Simplify and combine like terms.
Simplify each term.
Multiply 3 by 1.
(3+3(-4i)-i⋅1-i(-4i))(2+i)(2-i)(2+i)
Multiply -4 by 3.
(3-12i-i⋅1-i(-4i))(2+i)(2-i)(2+i)
Multiply -1 by 1.
(3-12i-i-i(-4i))(2+i)(2-i)(2+i)
Multiply -i(-4i).
Multiply -4 by -1.
(3-12i-i+4ii)(2+i)(2-i)(2+i)
Raise i to the power of 1.
(3-12i-i+4(i1i))(2+i)(2-i)(2+i)
Raise i to the power of 1.
(3-12i-i+4(i1i1))(2+i)(2-i)(2+i)
Use the power rule aman=am+n to combine exponents.
(3-12i-i+4i1+1)(2+i)(2-i)(2+i)
(3-12i-i+4i2)(2+i)(2-i)(2+i)
(3-12i-i+4i2)(2+i)(2-i)(2+i)
Rewrite i2 as -1.
(3-12i-i+4⋅-1)(2+i)(2-i)(2+i)
Multiply 4 by -1.
(3-12i-i-4)(2+i)(2-i)(2+i)
(3-12i-i-4)(2+i)(2-i)(2+i)
Subtract 4 from 3.
(-1-12i-i)(2+i)(2-i)(2+i)
Subtract i from -12i.
(-1-13i)(2+i)(2-i)(2+i)
(-1-13i)(2+i)(2-i)(2+i)
Expand (-1-13i)(2+i) using the FOIL Method.
Apply the distributive property.
-1(2+i)-13i(2+i)(2-i)(2+i)
Apply the distributive property.
-1⋅2-1i-13i(2+i)(2-i)(2+i)
Apply the distributive property.
-1⋅2-1i-13i⋅2-13ii(2-i)(2+i)
-1⋅2-1i-13i⋅2-13ii(2-i)(2+i)
Simplify and combine like terms.
Simplify each term.
Multiply -1 by 2.
-2-1i-13i⋅2-13ii(2-i)(2+i)
Rewrite -1i as -i.
-2-i-13i⋅2-13ii(2-i)(2+i)
Multiply 2 by -13.
-2-i-26i-13ii(2-i)(2+i)
Multiply -13ii.
Raise i to the power of 1.
-2-i-26i-13(i1i)(2-i)(2+i)
Raise i to the power of 1.
-2-i-26i-13(i1i1)(2-i)(2+i)
Use the power rule aman=am+n to combine exponents.
-2-i-26i-13i1+1(2-i)(2+i)
-2-i-26i-13i2(2-i)(2+i)
-2-i-26i-13i2(2-i)(2+i)
Rewrite i2 as -1.
-2-i-26i-13⋅-1(2-i)(2+i)
Multiply -13 by -1.
-2-i-26i+13(2-i)(2+i)
-2-i-26i+13(2-i)(2+i)
11-i-26i(2-i)(2+i)
Subtract 26i from -i.
11-27i(2-i)(2+i)
11-27i(2-i)(2+i)
11-27i(2-i)(2+i)
Simplify the denominator.
Expand (2-i)(2+i) using the FOIL Method.
Apply the distributive property.
11-27i2(2+i)-i(2+i)
Apply the distributive property.
11-27i2⋅2+2i-i(2+i)
Apply the distributive property.
11-27i2⋅2+2i-i⋅2-ii
11-27i2⋅2+2i-i⋅2-ii
Simplify.
Multiply 2 by 2.
11-27i4+2i-i⋅2-ii
Multiply 2 by -1.
11-27i4+2i-2i-ii
Raise i to the power of 1.
11-27i4+2i-2i-(i1i)
Raise i to the power of 1.
11-27i4+2i-2i-(i1i1)
Use the power rule aman=am+n to combine exponents.
11-27i4+2i-2i-i1+1
11-27i4+2i-2i-i2
Subtract 2i from 2i.
11-27i4+0-i2
11-27i4-i2
11-27i4-i2
Simplify each term.
Rewrite i2 as -1.
11-27i4–1
Multiply -1 by -1.
11-27i4+1
11-27i4+1
11-27i5
11-27i5
11-27i5
Split the fraction 11-27i5 into two fractions.
115+-27i5
Move the negative in front of the fraction.
115-27i5
Write in Standard Form ((3-i)(1-4i))/(2-i)

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