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raketka [301]
3 years ago
7

If (a+bi)^2=2abi, what must be the relationship between a and b? Show or explain your reasoning.

Mathematics
1 answer:
Klio2033 [76]3 years ago
6 0
(a+bi)^2 =(a+bi)(a+bi)= a^2 +2abi+b^2 i^2 \\  \\ i^2 = -1 \\  \\ (a+bi)^2 = a^2-b^2 +2abi = 2abi \\  \\ a^2 -b^2 = 0 \\  \\ a^2 = b^2 \\  \\ a = b

For the statement to be true, 'a' and 'b' must be equal

*First expand the binomial using FOIL, then set it equal to whats given "2abi".
Then you can find the relationship between a and b.
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Answer:1.36 for the chips

Step-by-step explanation:

15-9.99=5.01

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6 0
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Andrei [34K]

Answer:

34 + x = 70 ; 36

Step-by-step explanation:

Given that:

Current amount = 34

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Current amount + number planted today = final amount

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x = 36

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the measurement of an angle is five times less than the measurement of its supplement what is the measurement of the angle a. 30
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8 0
4 years ago
Determine which equation is belongs to the graph of the limacon curve below.
JulsSmile [24]

Answer: Option C.

Step-by-step explanation:

We have functions of r(θ)

In our graph, we can see that the minimum value of r is when θ = 0°, and the maximum value is when θ = 180°.

We also know that the graph is in the square (-5, 5)x(-5, 5) and you can see that the maximum radius is almost less than 5.

Then let's analyze the options:

A) r = 3 - 2*cos(θ)

the maximum is at the right angle, but the maximum is:

r = 3 -2*(-1) = 5, so this maximum value is bigger than the one in the graph.

B) r = 3 - sin(θ)

For the sin functions, the maximum and minimum do not correspond with the values i write earlier, so we can discard this option.

C) r = 3 - cos(θ)

The maximum is: r = 3 - (-1) = 4, so this may be the correct answer.

the minimum is r = 3 - 1 = 2,

this is a possible equation for our circle.

D) r = 2 - 2*cos(θ)

Here, when θ = 0, we have: r = 2 - 2*1 = 0, but in the graph we can see that the radius is not 0 when θ = 0, so we can discard this option.

So the only option that makes sense is option C.

8 0
3 years ago
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