## ashleyb 3 years ago simplify...pic is in comment box

1. ashleyb

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2. satellite73

$$(a+bi)(c+di)=(ac-bd)+(ad+bc)i$$ either that, or multiply out using four multiplications like you would with $$(x+2)(x+5)$$ and then at the end replace $$i^2$$ by $$-1$$

3. satellite73

here $$a=10,b=3, c=5,d=-2$$ so first method gives $(10\times 5-3\times (-2))+(10\times (-2)+3\times 5)i$

4. ashleyb

sorry but im still having trouble understanding

5. Ajk

I just FOILed and then combined like terms. So, 10 x 5 = 50, 10 x -2i = -20i, 3i x 5 = 15i, and 3i x -2i = -6i^2. Combining like terms gets me 50 - 5i -6i^2, but we then remember that i^2 = -1, so further simplifying becomes 50 - 5i + 6 ------> 56 - 5i. Did that make sense?