Simplify (3+10i)^2

Math
(3+10i)2
Rewrite (3+10i)2 as (3+10i)(3+10i).
(3+10i)(3+10i)
Expand (3+10i)(3+10i) using the FOIL Method.
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Apply the distributive property.
3(3+10i)+10i(3+10i)
Apply the distributive property.
3⋅3+3(10i)+10i(3+10i)
Apply the distributive property.
3⋅3+3(10i)+10i⋅3+10i(10i)
3⋅3+3(10i)+10i⋅3+10i(10i)
Simplify and combine like terms.
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Simplify each term.
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Multiply 3 by 3.
9+3(10i)+10i⋅3+10i(10i)
Multiply 10 by 3.
9+30i+10i⋅3+10i(10i)
Multiply 3 by 10.
9+30i+30i+10i(10i)
Multiply 10i(10i).
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Multiply 10 by 10.
9+30i+30i+100ii
Raise i to the power of 1.
9+30i+30i+100(i1i)
Raise i to the power of 1.
9+30i+30i+100(i1i1)
Use the power rule aman=am+n to combine exponents.
9+30i+30i+100i1+1
Add 1 and 1.
9+30i+30i+100i2
9+30i+30i+100i2
Rewrite i2 as -1.
9+30i+30i+100⋅-1
Multiply 100 by -1.
9+30i+30i-100
9+30i+30i-100
Subtract 100 from 9.
-91+30i+30i
Add 30i and 30i.
-91+60i
-91+60i
Simplify (3+10i)^2

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