Simplify (4-2i)(8+5i)

Math
(4-2i)(8+5i)
Expand (4-2i)(8+5i) using the FOIL Method.
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Apply the distributive property.
4(8+5i)-2i(8+5i)
Apply the distributive property.
4⋅8+4(5i)-2i(8+5i)
Apply the distributive property.
4⋅8+4(5i)-2i⋅8-2i(5i)
4⋅8+4(5i)-2i⋅8-2i(5i)
Simplify and combine like terms.
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Simplify each term.
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Multiply 4 by 8.
32+4(5i)-2i⋅8-2i(5i)
Multiply 5 by 4.
32+20i-2i⋅8-2i(5i)
Multiply 8 by -2.
32+20i-16i-2i(5i)
Multiply -2i(5i).
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Multiply 5 by -2.
32+20i-16i-10ii
Raise i to the power of 1.
32+20i-16i-10(i1i)
Raise i to the power of 1.
32+20i-16i-10(i1i1)
Use the power rule aman=am+n to combine exponents.
32+20i-16i-10i1+1
Add 1 and 1.
32+20i-16i-10i2
32+20i-16i-10i2
Rewrite i2 as -1.
32+20i-16i-10⋅-1
Multiply -10 by -1.
32+20i-16i+10
32+20i-16i+10
Add 32 and 10.
42+20i-16i
Subtract 16i from 20i.
42+4i
42+4i
Simplify (4-2i)(8+5i)

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