# Simplify (6i)/(8-7i)

6i8-7i
Multiply the numerator and denominator of 6i8-7i by the conjugate of 8-7i to make the denominator real.
6i8-7i⋅8+7i8+7i
Multiply.
Combine.
6i(8+7i)(8-7i)(8+7i)
Simplify the numerator.
Apply the distributive property.
6i⋅8+6i(7i)(8-7i)(8+7i)
Multiply 8 by 6.
48i+6i(7i)(8-7i)(8+7i)
Multiply 6i(7i).
Multiply 7 by 6.
48i+42ii(8-7i)(8+7i)
Raise i to the power of 1.
48i+42(i1i)(8-7i)(8+7i)
Raise i to the power of 1.
48i+42(i1i1)(8-7i)(8+7i)
Use the power rule aman=am+n to combine exponents.
48i+42i1+1(8-7i)(8+7i)
Add 1 and 1.
48i+42i2(8-7i)(8+7i)
48i+42i2(8-7i)(8+7i)
Simplify each term.
Rewrite i2 as -1.
48i+42⋅-1(8-7i)(8+7i)
Multiply 42 by -1.
48i-42(8-7i)(8+7i)
48i-42(8-7i)(8+7i)
Reorder 48i and -42.
-42+48i(8-7i)(8+7i)
-42+48i(8-7i)(8+7i)
Simplify the denominator.
Expand (8-7i)(8+7i) using the FOIL Method.
Apply the distributive property.
-42+48i8(8+7i)-7i(8+7i)
Apply the distributive property.
-42+48i8⋅8+8(7i)-7i(8+7i)
Apply the distributive property.
-42+48i8⋅8+8(7i)-7i⋅8-7i(7i)
-42+48i8⋅8+8(7i)-7i⋅8-7i(7i)
Simplify.
Multiply 8 by 8.
-42+48i64+8(7i)-7i⋅8-7i(7i)
Multiply 7 by 8.
-42+48i64+56i-7i⋅8-7i(7i)
Multiply 8 by -7.
-42+48i64+56i-56i-7i(7i)
Multiply 7 by -7.
-42+48i64+56i-56i-49ii
Raise i to the power of 1.
-42+48i64+56i-56i-49(i1i)
Raise i to the power of 1.
-42+48i64+56i-56i-49(i1i1)
Use the power rule aman=am+n to combine exponents.
-42+48i64+56i-56i-49i1+1
Add 1 and 1.
-42+48i64+56i-56i-49i2
Subtract 56i from 56i.
-42+48i64+0-49i2
Add 64 and 0.
-42+48i64-49i2
-42+48i64-49i2
Simplify each term.
Rewrite i2 as -1.
-42+48i64-49⋅-1
Multiply -49 by -1.
-42+48i64+49
-42+48i64+49
Add 64 and 49.
-42+48i113
-42+48i113
-42+48i113
Split the fraction -42+48i113 into two fractions.
-42113+48i113
Move the negative in front of the fraction.
-42113+48i113
Simplify (6i)/(8-7i)

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