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gulaghasi [49]
3 years ago
11

For what value of "a" will the product shown below have a purely imaginary value? (Show work please)

Mathematics
1 answer:
MakcuM [25]3 years ago
5 0
If you expand out the brackets you get this,

(4+5i)(a+2i) = 4a + (5a)i + 8i - 10

The -10 comes from 5i * 2i.
Squaring i becomes -1.

Let's group the real stuff together,
and imaginary separately,

(4a - 10) + (5a + 8)i

For this to be purely imaginary,
the real part needs to be zero.

Therefore 4a - 10 = 0

Solve for a.
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1. Given ΔQRS (is congruent to) ΔTUV, QS = 3v + 2 and TV = 7v - 6, find the length of QS and TV. Provide a detailed response bel
Morgarella [4.7K]
Because ΔQRS is congruent to <span>ΔTUV, the the segments GS and TV are also congruent due to the letter order (Q and T are first and S and V are 3rd.) Since they are congruent QS=TV. So 3v + 2 = 7v - 6
</span><span>
</span><span>Work: 
</span>3v + 2 = 7v - 6
      +6          +6
3v + 8=7v
-3v       -3v
<u>8</u> = <span><u>4v</u>
</span>4      4
2 = v

3(2) + 2 = GS
6+2 = GS
8 = GS

7(2) - 6 = TV
14-6=TV
8 = TV

Final Answer: 8=QS and 8=TV

 
3 0
3 years ago
Read 2 more answers
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