Write in Standard Form (4+5i)/(1-3i)

Math
4+5i1-3i
Multiply the numerator and denominator of 4+5i1-3i by the conjugate of 1-3i to make the denominator real.
4+5i1-3i⋅1+3i1+3i
Multiply.
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Combine.
(4+5i)(1+3i)(1-3i)(1+3i)
Simplify the numerator.
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Expand (4+5i)(1+3i) using the FOIL Method.
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Apply the distributive property.
4(1+3i)+5i(1+3i)(1-3i)(1+3i)
Apply the distributive property.
4⋅1+4(3i)+5i(1+3i)(1-3i)(1+3i)
Apply the distributive property.
4⋅1+4(3i)+5i⋅1+5i(3i)(1-3i)(1+3i)
4⋅1+4(3i)+5i⋅1+5i(3i)(1-3i)(1+3i)
Simplify and combine like terms.
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Simplify each term.
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Multiply 4 by 1.
4+4(3i)+5i⋅1+5i(3i)(1-3i)(1+3i)
Multiply 3 by 4.
4+12i+5i⋅1+5i(3i)(1-3i)(1+3i)
Multiply 5 by 1.
4+12i+5i+5i(3i)(1-3i)(1+3i)
Multiply 5i(3i).
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Multiply 3 by 5.
4+12i+5i+15ii(1-3i)(1+3i)
Raise i to the power of 1.
4+12i+5i+15(i1i)(1-3i)(1+3i)
Raise i to the power of 1.
4+12i+5i+15(i1i1)(1-3i)(1+3i)
Use the power rule aman=am+n to combine exponents.
4+12i+5i+15i1+1(1-3i)(1+3i)
Add 1 and 1.
4+12i+5i+15i2(1-3i)(1+3i)
4+12i+5i+15i2(1-3i)(1+3i)
Rewrite i2 as -1.
4+12i+5i+15⋅-1(1-3i)(1+3i)
Multiply 15 by -1.
4+12i+5i-15(1-3i)(1+3i)
4+12i+5i-15(1-3i)(1+3i)
Subtract 15 from 4.
-11+12i+5i(1-3i)(1+3i)
Add 12i and 5i.
-11+17i(1-3i)(1+3i)
-11+17i(1-3i)(1+3i)
-11+17i(1-3i)(1+3i)
Simplify the denominator.
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Expand (1-3i)(1+3i) using the FOIL Method.
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Apply the distributive property.
-11+17i1(1+3i)-3i(1+3i)
Apply the distributive property.
-11+17i1⋅1+1(3i)-3i(1+3i)
Apply the distributive property.
-11+17i1⋅1+1(3i)-3i⋅1-3i(3i)
-11+17i1⋅1+1(3i)-3i⋅1-3i(3i)
Simplify.
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Multiply 1 by 1.
-11+17i1+1(3i)-3i⋅1-3i(3i)
Multiply 3 by 1.
-11+17i1+3i-3i⋅1-3i(3i)
Multiply -3 by 1.
-11+17i1+3i-3i-3i(3i)
Multiply 3 by -3.
-11+17i1+3i-3i-9ii
Raise i to the power of 1.
-11+17i1+3i-3i-9(i1i)
Raise i to the power of 1.
-11+17i1+3i-3i-9(i1i1)
Use the power rule aman=am+n to combine exponents.
-11+17i1+3i-3i-9i1+1
Add 1 and 1.
-11+17i1+3i-3i-9i2
Subtract 3i from 3i.
-11+17i1+0-9i2
Add 1 and 0.
-11+17i1-9i2
-11+17i1-9i2
Simplify each term.
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Rewrite i2 as -1.
-11+17i1-9⋅-1
Multiply -9 by -1.
-11+17i1+9
-11+17i1+9
Add 1 and 9.
-11+17i10
-11+17i10
-11+17i10
Split the fraction -11+17i10 into two fractions.
-1110+17i10
Move the negative in front of the fraction.
-1110+17i10
Write in Standard Form (4+5i)/(1-3i)

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