Simplify (5+6i)(8+4i)

Math
(5+6i)(8+4i)
Expand (5+6i)(8+4i) using the FOIL Method.
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Apply the distributive property.
5(8+4i)+6i(8+4i)
Apply the distributive property.
5⋅8+5(4i)+6i(8+4i)
Apply the distributive property.
5⋅8+5(4i)+6i⋅8+6i(4i)
5⋅8+5(4i)+6i⋅8+6i(4i)
Simplify and combine like terms.
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Simplify each term.
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Multiply 5 by 8.
40+5(4i)+6i⋅8+6i(4i)
Multiply 4 by 5.
40+20i+6i⋅8+6i(4i)
Multiply 8 by 6.
40+20i+48i+6i(4i)
Multiply 6i(4i).
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Multiply 4 by 6.
40+20i+48i+24ii
Raise i to the power of 1.
40+20i+48i+24(i1i)
Raise i to the power of 1.
40+20i+48i+24(i1i1)
Use the power rule aman=am+n to combine exponents.
40+20i+48i+24i1+1
Add 1 and 1.
40+20i+48i+24i2
40+20i+48i+24i2
Rewrite i2 as -1.
40+20i+48i+24⋅-1
Multiply 24 by -1.
40+20i+48i-24
40+20i+48i-24
Subtract 24 from 40.
16+20i+48i
Add 20i and 48i.
16+68i
16+68i
Simplify (5+6i)(8+4i)

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