Rewrite in Standard Form (1-4i)/(3-i)

Math
1-4i3-i
Multiply the numerator and denominator of 1-4i3-i by the conjugate of 3-i to make the denominator real.
1-4i3-i⋅3+i3+i
Multiply.
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Combine.
(1-4i)(3+i)(3-i)(3+i)
Simplify the numerator.
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Expand (1-4i)(3+i) using the FOIL Method.
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Apply the distributive property.
1(3+i)-4i(3+i)(3-i)(3+i)
Apply the distributive property.
1⋅3+1i-4i(3+i)(3-i)(3+i)
Apply the distributive property.
1⋅3+1i-4i⋅3-4ii(3-i)(3+i)
1⋅3+1i-4i⋅3-4ii(3-i)(3+i)
Simplify and combine like terms.
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Simplify each term.
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Multiply 3 by 1.
3+1i-4i⋅3-4ii(3-i)(3+i)
Multiply i by 1.
3+i-4i⋅3-4ii(3-i)(3+i)
Multiply 3 by -4.
3+i-12i-4ii(3-i)(3+i)
Multiply -4ii.
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Raise i to the power of 1.
3+i-12i-4(i1i)(3-i)(3+i)
Raise i to the power of 1.
3+i-12i-4(i1i1)(3-i)(3+i)
Use the power rule aman=am+n to combine exponents.
3+i-12i-4i1+1(3-i)(3+i)
Add 1 and 1.
3+i-12i-4i2(3-i)(3+i)
3+i-12i-4i2(3-i)(3+i)
Rewrite i2 as -1.
3+i-12i-4⋅-1(3-i)(3+i)
Multiply -4 by -1.
3+i-12i+4(3-i)(3+i)
3+i-12i+4(3-i)(3+i)
Add 3 and 4.
7+i-12i(3-i)(3+i)
Subtract 12i from i.
7-11i(3-i)(3+i)
7-11i(3-i)(3+i)
7-11i(3-i)(3+i)
Simplify the denominator.
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Expand (3-i)(3+i) using the FOIL Method.
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Apply the distributive property.
7-11i3(3+i)-i(3+i)
Apply the distributive property.
7-11i3⋅3+3i-i(3+i)
Apply the distributive property.
7-11i3⋅3+3i-i⋅3-ii
7-11i3⋅3+3i-i⋅3-ii
Simplify.
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Multiply 3 by 3.
7-11i9+3i-i⋅3-ii
Multiply 3 by -1.
7-11i9+3i-3i-ii
Raise i to the power of 1.
7-11i9+3i-3i-(i1i)
Raise i to the power of 1.
7-11i9+3i-3i-(i1i1)
Use the power rule aman=am+n to combine exponents.
7-11i9+3i-3i-i1+1
Add 1 and 1.
7-11i9+3i-3i-i2
Subtract 3i from 3i.
7-11i9+0-i2
Add 9 and 0.
7-11i9-i2
7-11i9-i2
Simplify each term.
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Rewrite i2 as -1.
7-11i9–1
Multiply -1 by -1.
7-11i9+1
7-11i9+1
Add 9 and 1.
7-11i10
7-11i10
7-11i10
Split the fraction 7-11i10 into two fractions.
710+-11i10
Move the negative in front of the fraction.
710-11i10
Rewrite in Standard Form (1-4i)/(3-i)

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