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

Combine.

(2-7i)(9-i)(9+1i)(9-i)

Simplify the numerator.

Expand (2-7i)(9-i) using the FOIL Method.

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.

Simplify each term.

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).

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.

Expand (9+1i)(9-i) using the FOIL Method.

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.

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.

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)