What is (Oe+Oi)(Di+De) ?

The solution to (Oe+Oi)(Di+De) is (e^2DO-DO)+2eiDO

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simplify (Oe+Oi)(Di+De)

simplify

(O e + O i) (D i + De)

(e^{2} D O - D O) + 2 e i D O

Solution steps

(O e + O i) (D i + De)

Apply complex arithmetic rule:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

a = O e, b = O, c = De, d = D

= (O eDe - O D) + (O eD + O De) i

Simplify

O eDe - O D : e^{2} D O - D O

Simplify

O eD + O De : 2 eD O

= (e^{2} D O - D O) + 2 eD O i

Remove parentheses:

(a) = a

= e^{2} D O - D O + 2 eD O i

Rewrite

e^{2} D O - D O + 2 eD O i

in standard complex form:

(e^{2} D O - D O) + 2 eD O i

= (e^{2} D O - D O) + 2 eD O i

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