Rewrite in Standard Form (6+5i)/(2-i)

Math
6+5i2-i
Multiply the numerator and denominator of 6+5i2-i by the conjugate of 2-i to make the denominator real.
6+5i2-i⋅2+i2+i
Multiply.
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Combine.
(6+5i)(2+i)(2-i)(2+i)
Simplify the numerator.
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Expand (6+5i)(2+i) using the FOIL Method.
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Apply the distributive property.
6(2+i)+5i(2+i)(2-i)(2+i)
Apply the distributive property.
6⋅2+6i+5i(2+i)(2-i)(2+i)
Apply the distributive property.
6⋅2+6i+5i⋅2+5ii(2-i)(2+i)
6⋅2+6i+5i⋅2+5ii(2-i)(2+i)
Simplify and combine like terms.
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Simplify each term.
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Multiply 6 by 2.
12+6i+5i⋅2+5ii(2-i)(2+i)
Multiply 2 by 5.
12+6i+10i+5ii(2-i)(2+i)
Multiply 5ii.
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Raise i to the power of 1.
12+6i+10i+5(i1i)(2-i)(2+i)
Raise i to the power of 1.
12+6i+10i+5(i1i1)(2-i)(2+i)
Use the power rule aman=am+n to combine exponents.
12+6i+10i+5i1+1(2-i)(2+i)
Add 1 and 1.
12+6i+10i+5i2(2-i)(2+i)
12+6i+10i+5i2(2-i)(2+i)
Rewrite i2 as -1.
12+6i+10i+5⋅-1(2-i)(2+i)
Multiply 5 by -1.
12+6i+10i-5(2-i)(2+i)
12+6i+10i-5(2-i)(2+i)
Subtract 5 from 12.
7+6i+10i(2-i)(2+i)
Add 6i and 10i.
7+16i(2-i)(2+i)
7+16i(2-i)(2+i)
7+16i(2-i)(2+i)
Simplify the denominator.
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Expand (2-i)(2+i) using the FOIL Method.
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Apply the distributive property.
7+16i2(2+i)-i(2+i)
Apply the distributive property.
7+16i2⋅2+2i-i(2+i)
Apply the distributive property.
7+16i2⋅2+2i-i⋅2-ii
7+16i2⋅2+2i-i⋅2-ii
Simplify.
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Multiply 2 by 2.
7+16i4+2i-i⋅2-ii
Multiply 2 by -1.
7+16i4+2i-2i-ii
Raise i to the power of 1.
7+16i4+2i-2i-(i1i)
Raise i to the power of 1.
7+16i4+2i-2i-(i1i1)
Use the power rule aman=am+n to combine exponents.
7+16i4+2i-2i-i1+1
Add 1 and 1.
7+16i4+2i-2i-i2
Subtract 2i from 2i.
7+16i4+0-i2
Add 4 and 0.
7+16i4-i2
7+16i4-i2
Simplify each term.
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Rewrite i2 as -1.
7+16i4–1
Multiply -1 by -1.
7+16i4+1
7+16i4+1
Add 4 and 1.
7+16i5
7+16i5
7+16i5
Split the fraction 7+16i5 into two fractions.
75+16i5
Rewrite in Standard Form (6+5i)/(2-i)

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