5-3i4+3i

Multiply the numerator and denominator of 5-3i4+3i by the conjugate of 4+3i to make the denominator real.

5-3i4+3i⋅4-3i4-3i

Combine.

(5-3i)(4-3i)(4+3i)(4-3i)

Simplify the numerator.

Expand (5-3i)(4-3i) using the FOIL Method.

Apply the distributive property.

5(4-3i)-3i(4-3i)(4+3i)(4-3i)

Apply the distributive property.

5⋅4+5(-3i)-3i(4-3i)(4+3i)(4-3i)

Apply the distributive property.

5⋅4+5(-3i)-3i⋅4-3i(-3i)(4+3i)(4-3i)

5⋅4+5(-3i)-3i⋅4-3i(-3i)(4+3i)(4-3i)

Simplify and combine like terms.

Simplify each term.

Multiply 5 by 4.

20+5(-3i)-3i⋅4-3i(-3i)(4+3i)(4-3i)

Multiply -3 by 5.

20-15i-3i⋅4-3i(-3i)(4+3i)(4-3i)

Multiply 4 by -3.

20-15i-12i-3i(-3i)(4+3i)(4-3i)

Multiply -3i(-3i).

Multiply -3 by -3.

20-15i-12i+9ii(4+3i)(4-3i)

Raise i to the power of 1.

20-15i-12i+9(i1i)(4+3i)(4-3i)

Raise i to the power of 1.

20-15i-12i+9(i1i1)(4+3i)(4-3i)

Use the power rule aman=am+n to combine exponents.

20-15i-12i+9i1+1(4+3i)(4-3i)

Add 1 and 1.

20-15i-12i+9i2(4+3i)(4-3i)

20-15i-12i+9i2(4+3i)(4-3i)

Rewrite i2 as -1.

20-15i-12i+9⋅-1(4+3i)(4-3i)

Multiply 9 by -1.

20-15i-12i-9(4+3i)(4-3i)

20-15i-12i-9(4+3i)(4-3i)

Subtract 9 from 20.

11-15i-12i(4+3i)(4-3i)

Subtract 12i from -15i.

11-27i(4+3i)(4-3i)

11-27i(4+3i)(4-3i)

11-27i(4+3i)(4-3i)

Simplify the denominator.

Expand (4+3i)(4-3i) using the FOIL Method.

Apply the distributive property.

11-27i4(4-3i)+3i(4-3i)

Apply the distributive property.

11-27i4⋅4+4(-3i)+3i(4-3i)

Apply the distributive property.

11-27i4⋅4+4(-3i)+3i⋅4+3i(-3i)

11-27i4⋅4+4(-3i)+3i⋅4+3i(-3i)

Simplify.

Multiply 4 by 4.

11-27i16+4(-3i)+3i⋅4+3i(-3i)

Multiply -3 by 4.

11-27i16-12i+3i⋅4+3i(-3i)

Multiply 4 by 3.

11-27i16-12i+12i+3i(-3i)

Multiply -3 by 3.

11-27i16-12i+12i-9ii

Raise i to the power of 1.

11-27i16-12i+12i-9(i1i)

Raise i to the power of 1.

11-27i16-12i+12i-9(i1i1)

Use the power rule aman=am+n to combine exponents.

11-27i16-12i+12i-9i1+1

Add 1 and 1.

11-27i16-12i+12i-9i2

Add -12i and 12i.

11-27i16+0-9i2

Add 16 and 0.

11-27i16-9i2

11-27i16-9i2

Simplify each term.

Rewrite i2 as -1.

11-27i16-9⋅-1

Multiply -9 by -1.

11-27i16+9

11-27i16+9

Add 16 and 9.

11-27i25

11-27i25

11-27i25

Split the fraction 11-27i25 into two fractions.

1125+-27i25

Move the negative in front of the fraction.

1125-27i25

Write in Standard Form (5-3i)/(4+3i)