Rewrite in Standard Form (4+5i)/(6-5i)

Math
4+5i6-5i
Multiply the numerator and denominator of 4+5i6-5i by the conjugate of 6-5i to make the denominator real.
4+5i6-5i⋅6+5i6+5i
Multiply.
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Combine.
(4+5i)(6+5i)(6-5i)(6+5i)
Simplify the numerator.
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Expand (4+5i)(6+5i) using the FOIL Method.
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Apply the distributive property.
4(6+5i)+5i(6+5i)(6-5i)(6+5i)
Apply the distributive property.
4⋅6+4(5i)+5i(6+5i)(6-5i)(6+5i)
Apply the distributive property.
4⋅6+4(5i)+5i⋅6+5i(5i)(6-5i)(6+5i)
4⋅6+4(5i)+5i⋅6+5i(5i)(6-5i)(6+5i)
Simplify and combine like terms.
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Simplify each term.
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Multiply 4 by 6.
24+4(5i)+5i⋅6+5i(5i)(6-5i)(6+5i)
Multiply 5 by 4.
24+20i+5i⋅6+5i(5i)(6-5i)(6+5i)
Multiply 6 by 5.
24+20i+30i+5i(5i)(6-5i)(6+5i)
Multiply 5i(5i).
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Multiply 5 by 5.
24+20i+30i+25ii(6-5i)(6+5i)
Raise i to the power of 1.
24+20i+30i+25(i1i)(6-5i)(6+5i)
Raise i to the power of 1.
24+20i+30i+25(i1i1)(6-5i)(6+5i)
Use the power rule aman=am+n to combine exponents.
24+20i+30i+25i1+1(6-5i)(6+5i)
Add 1 and 1.
24+20i+30i+25i2(6-5i)(6+5i)
24+20i+30i+25i2(6-5i)(6+5i)
Rewrite i2 as -1.
24+20i+30i+25⋅-1(6-5i)(6+5i)
Multiply 25 by -1.
24+20i+30i-25(6-5i)(6+5i)
24+20i+30i-25(6-5i)(6+5i)
Subtract 25 from 24.
-1+20i+30i(6-5i)(6+5i)
Add 20i and 30i.
-1+50i(6-5i)(6+5i)
-1+50i(6-5i)(6+5i)
-1+50i(6-5i)(6+5i)
Simplify the denominator.
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Expand (6-5i)(6+5i) using the FOIL Method.
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Apply the distributive property.
-1+50i6(6+5i)-5i(6+5i)
Apply the distributive property.
-1+50i6⋅6+6(5i)-5i(6+5i)
Apply the distributive property.
-1+50i6⋅6+6(5i)-5i⋅6-5i(5i)
-1+50i6⋅6+6(5i)-5i⋅6-5i(5i)
Simplify.
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Multiply 6 by 6.
-1+50i36+6(5i)-5i⋅6-5i(5i)
Multiply 5 by 6.
-1+50i36+30i-5i⋅6-5i(5i)
Multiply 6 by -5.
-1+50i36+30i-30i-5i(5i)
Multiply 5 by -5.
-1+50i36+30i-30i-25ii
Raise i to the power of 1.
-1+50i36+30i-30i-25(i1i)
Raise i to the power of 1.
-1+50i36+30i-30i-25(i1i1)
Use the power rule aman=am+n to combine exponents.
-1+50i36+30i-30i-25i1+1
Add 1 and 1.
-1+50i36+30i-30i-25i2
Subtract 30i from 30i.
-1+50i36+0-25i2
Add 36 and 0.
-1+50i36-25i2
-1+50i36-25i2
Simplify each term.
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Rewrite i2 as -1.
-1+50i36-25⋅-1
Multiply -25 by -1.
-1+50i36+25
-1+50i36+25
Add 36 and 25.
-1+50i61
-1+50i61
-1+50i61
Split the fraction -1+50i61 into two fractions.
-161+50i61
Move the negative in front of the fraction.
-161+50i61
Rewrite in Standard Form (4+5i)/(6-5i)

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