Write in Standard Form (2-7i)/(9+i)

Math
2-7i9+i
Multiply the numerator and denominator of 2-7i9+1i by the conjugate of 9+1i to make the denominator real.
2-7i9+1i⋅9-i9-i
Multiply.
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Combine.
(2-7i)(9-i)(9+1i)(9-i)
Simplify the numerator.
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Expand (2-7i)(9-i) using the FOIL Method.
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Apply the distributive property.
2(9-i)-7i(9-i)(9+1i)(9-i)
Apply the distributive property.
2⋅9+2(-i)-7i(9-i)(9+1i)(9-i)
Apply the distributive property.
2⋅9+2(-i)-7i⋅9-7i(-i)(9+1i)(9-i)
2⋅9+2(-i)-7i⋅9-7i(-i)(9+1i)(9-i)
Simplify and combine like terms.
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Simplify each term.
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Multiply 2 by 9.
18+2(-i)-7i⋅9-7i(-i)(9+1i)(9-i)
Multiply -1 by 2.
18-2i-7i⋅9-7i(-i)(9+1i)(9-i)
Multiply 9 by -7.
18-2i-63i-7i(-i)(9+1i)(9-i)
Multiply -7i(-i).
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Multiply -1 by -7.
18-2i-63i+7ii(9+1i)(9-i)
Raise i to the power of 1.
18-2i-63i+7(i1i)(9+1i)(9-i)
Raise i to the power of 1.
18-2i-63i+7(i1i1)(9+1i)(9-i)
Use the power rule aman=am+n to combine exponents.
18-2i-63i+7i1+1(9+1i)(9-i)
Add 1 and 1.
18-2i-63i+7i2(9+1i)(9-i)
18-2i-63i+7i2(9+1i)(9-i)
Rewrite i2 as -1.
18-2i-63i+7⋅-1(9+1i)(9-i)
Multiply 7 by -1.
18-2i-63i-7(9+1i)(9-i)
18-2i-63i-7(9+1i)(9-i)
Subtract 7 from 18.
11-2i-63i(9+1i)(9-i)
Subtract 63i from -2i.
11-65i(9+1i)(9-i)
11-65i(9+1i)(9-i)
11-65i(9+1i)(9-i)
Simplify the denominator.
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Expand (9+1i)(9-i) using the FOIL Method.
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Apply the distributive property.
11-65i9(9-i)+1i(9-i)
Apply the distributive property.
11-65i9⋅9+9(-i)+1i(9-i)
Apply the distributive property.
11-65i9⋅9+9(-i)+1i⋅9+1i(-i)
11-65i9⋅9+9(-i)+1i⋅9+1i(-i)
Simplify.
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Multiply 9 by 9.
11-65i81+9(-i)+1i⋅9+1i(-i)
Multiply -1 by 9.
11-65i81-9i+1i⋅9+1i(-i)
Multiply 9 by 1.
11-65i81-9i+9i+1i(-i)
Multiply -1 by 1.
11-65i81-9i+9i-ii
Raise i to the power of 1.
11-65i81-9i+9i-(i1i)
Raise i to the power of 1.
11-65i81-9i+9i-(i1i1)
Use the power rule aman=am+n to combine exponents.
11-65i81-9i+9i-i1+1
Add 1 and 1.
11-65i81-9i+9i-i2
Add -9i and 9i.
11-65i81+0-i2
Add 81 and 0.
11-65i81-i2
11-65i81-i2
Simplify each term.
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Rewrite i2 as -1.
11-65i81–1
Multiply -1 by -1.
11-65i81+1
11-65i81+1
Add 81 and 1.
11-65i82
11-65i82
11-65i82
Split the fraction 11-65i82 into two fractions.
1182+-65i82
Move the negative in front of the fraction.
1182-65i82
Write in Standard Form (2-7i)/(9+i)

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