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

Math
(4-5i)(2+i)
Expand (4-5i)(2+i) using the FOIL Method.
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Apply the distributive property.
4(2+i)-5i(2+i)
Apply the distributive property.
4⋅2+4i-5i(2+i)
Apply the distributive property.
4⋅2+4i-5i⋅2-5ii
4⋅2+4i-5i⋅2-5ii
Simplify and combine like terms.
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Simplify each term.
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Multiply 4 by 2.
8+4i-5i⋅2-5ii
Multiply 2 by -5.
8+4i-10i-5ii
Multiply -5ii.
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Raise i to the power of 1.
8+4i-10i-5(i1i)
Raise i to the power of 1.
8+4i-10i-5(i1i1)
Use the power rule aman=am+n to combine exponents.
8+4i-10i-5i1+1
Add 1 and 1.
8+4i-10i-5i2
8+4i-10i-5i2
Rewrite i2 as -1.
8+4i-10i-5⋅-1
Multiply -5 by -1.
8+4i-10i+5
8+4i-10i+5
Add 8 and 5.
13+4i-10i
Subtract 10i from 4i.
13-6i
13-6i
Simplify (4-5i)(2+i)

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