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puteri [66]
3 years ago
10

If A = -3 + 5i, B = 4 - 2i, and C = 1 +6i, where i is the imaginary unit, then A - BC equals

Mathematics
1 answer:
Maslowich3 years ago
6 0

Answer:

3) -19 - 17i is our answer

Step-by-step explanation:

to solve A - BC we plug in the values given

A= -3 + 5i

B = 4 - 2i

C = 1 + 6i

-3 + 51i - (4 - 2i)(1 + 6i) is our expression. we can FOIL (4 - 2i)(1 + 6i) this expression out. FOIL stands for:

First

Outside

Inside

Last

i will highlight the terms i am using in the current step in bold and put the result next of those two terms next to the expression

F: (4 - 2i)(1 + 6i) = 4

O: (4 - 2i)(1 + 6i) = 24i

I: (4 - 2i)(1 + 6i) = -2i

L: (4 - 2i)(1 + 6i) = 12 < --- the reason why its 12 and not -12i or 12i is because <em>i</em> = √-1 and i² = -1

when we multiply -2i * 6i, we would have gotten a -12i², and i² = -1, so we are multiplying -12 by -1, which gives us 12 as the result

combining all these terms together and we have:

4 + 24i - 2i + 12

in the expression this is:

-3 + 5i - (4 + 24i - 2i + 12) < we need to distribute the negative sign into (4 + 24i - 2i + 12) and we now get:

-3 + 5i -4 - 24i + 2i - 12 < combine like terms (ex: i terms together)

-3 - 4 - 12 = -19

5i - 24i + 2i = -17i

the result of the expression is:

-19 - 17i

we cannot simplify this any further so this is our answer. the answer choice that matches this is 3, so 3) -19 - 17i is our answer

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3 years ago
An exterior angle of a regular convex polygon is 40°. What is the number of sides of the polygon?
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Answer:

option B

Step-by-step explanation:

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Therefore, Each \ interior \  angle = (\frac{n - 2}{n} )\times 180

Sum \  of \  one \  of \  the  \ interior \  angle \  with  \ its  \ exterior \  angle \  is \  180^\circ

                      [ \ because \ straight \ line \ angle = 180^\circ \ ]

That is ,

Exterior \ angle + Interior \ angle = 180^\circ\\\\40^ \circ + (\frac{n-2}{n}) \times 180  = 180^\circ\\\\40 n + 180n - 360 = 180n\\\\40n = 180n - 180n + 360 \\\\40n = 360 \\\\n = 9

OR

Sum of exterior angles of a regular polygon = 360

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Therefore ,

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8 0
3 years ago
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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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So, use the x and y values of the points given and substitute them in the correct order into the formula:

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8 0
3 years ago
Find the cube roots of 125(cos 288° + i sin 288°)
kow [346]
Let r(cos O + i sin O)  be a cube root of 125(cos 288 + i sin 288)
then
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so r^3 = 125  and  cos 3O + i sin 3O  =  cos 288 + i sin 288

so r  = 5  and 3O = 288 + 360p and O = 96 +  120p

so one cube root is   5 (cos 96 + i sin 96)

Im a little rusty at this stuff Its been a long time.

Im not sure of the other 2 roots

sorry cant help you any more


3 0
3 years ago
Read 2 more answers
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