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# complex numbers

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If Q = 11 - 5i, E = 3 - 2i, and D = 2i, find QED.

May 9, 2021

#1
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$$QED = (11-5i)(3-2i)(2i)$$

We can split this up into two parts. Let's first compute $$(11-5i)(3-2i)$$, and then multiply it again by $$2i$$.

$$(11-5i)(3-2i) = 11(3-2i)-5i(3-2i) = 33-22i-15i+10i^2 = 33-37i-10 = 23-37i.$$

$$2i\cdot(23-37i) = 46i-74i^2 = \boxed{74+46i}$$

May 9, 2021