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

Math
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
Multiply.
Tap for more steps…
Combine.
(5-3i)(4-3i)(4+3i)(4-3i)
Simplify the numerator.
Tap for more steps…
Expand (5-3i)(4-3i) using the FOIL Method.
Tap for more steps…
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.
Tap for more steps…
Simplify each term.
Tap for more steps…
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).
Tap for more steps…
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.
Tap for more steps…
Expand (4+3i)(4-3i) using the FOIL Method.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
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)

Solving MATH problems

We can solve all math problems. Get help on the web or with our math app

Scroll to top