All categories

4 years ago

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

1 answer:

Klio2033 [76]4 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.

You might be interested in

WILL MARK BRAINLIEST ANSWER!

Vilka [71]

Answer:

D: 6/36

Step-by-step explanation:

As we are given the sample space, the events that sum to 6 are:

{(1,5), (2,4), (3,3),(4,2),(5,1)}

Let n(S) be the number of items in sample spae

n(S) = 36

Let E be the event the sum is 6

Then,

n(E) = 6

So,

P(Sum of two cubes is 6) = n(E) / n(S)

= 6/36

So, the correct answer is:

D: 6/36 ..

7 0

3 years ago

Read 2 more answers

please answer asap! A couple plans to have 5 children. The gender of each child is equally likely. Design a simulation involving

dimulka [17.4K]

Step-by-step explanation:

The gender of a child which is either a boy or a girl is determined by the XX-chromosomes, or XY-chromosomes.

Since the couple plan to have 5 children, the chance of a child being a boy is equal to the chance of it being a girl - the chances are 50/50.

What we do to achieve our aim is to run a simulation that would add an X or Y to an X for all 5 children.

Doing this 125 times, we obtain the number of trials we desire.

For each trial, we get for each child, C:

C1: X + (X or Y)

C2: X + (X or Y)

C3: X + (X or Y)

C4: X + (X or Y)

C5: X + (X or Y)

Since the chance of having an X is equal to the chance of having a Y, they equal probability, which is 0.5 for each.

6 0

3 years ago

−4/9f = −3 what does f equal?

solmaris [256]

Answer:

$\frac{27}{4}$ or 6.75

Step-by-step explanation:

To cancel out a fraction you multiply by the reciprocal. To make multiplying easier you can make -3 into a fraction by putting 1 under it
Multiplying across, two negatives make a positive so the answer is positive

$(-\frac{9}{4})-\frac{4}{9}f=-\frac{3}{1} (-\frac{9}{4})$

$f=\frac{27}{4}$

6 0

3 years ago

Find the area of the circle below???

olga55 [171]

Answer:

Area of the circle = $24.618\,feet^2$

Step-by-step explanation:

Radius of the circle= $2.8\,feet$

Area of the circle= $\pi \times r^2$

As,

$\pi =\dfrac{22}{7} =3.14$

Area of the circle is:

$=3.14\times 2.8 \times 2.8\\\\= 3.14 \times 7.84\\\\=24.618\,feet^2$

The Area of the circle is : $24.618\,feet^2$

5 0

3 years ago

Read 2 more answers

Find the missing factor.<br> 7s^2 + + 13s + 6 = (7s + 6)<br> )

Anton [14]

Answer:

71s

Step-by-step explanation:

The question we have at hand is 7s² + ___ + 13s + 6² = (7s + 6)². We can expand the perfect equation " (7s + 6)² " in order to find our solution. A perfect square consists of 3 terms, and hence the term in the blanks must add to 13s to form another term.

Applying the perfect square formula : ( a + b )² = a² + 2ab + b², let's expand the expression,

(7s + 6)² = ( 7s )² + 2( 7s )( 6 ) + ( 6 )² = 7s² + 84s + 6²

84s - 13s = 71s, which fills in the blank provided.

5 0

3 years ago