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2 years ago

12

Solve for z, and give your answer in the form a + bi

1 answer:

zzz [600]2 years ago

5 0

The answer is z = 3 + i

z = a + bi
conj(z) = a - bi

conj(7 + 3i) = 7 - 3i

<span>(conj)z + 2z = 2 + 4i + conj(7 + 3i)
</span>a - bi + 2(a + bi) =<span> 2 + 4i + 7 - 3i
</span>a - bi + 2a + 2bi =<span> 2 + 4i + 7 - 3i
</span>3a + bi = 9 + i

From here:
3a = 9 and bi = i
a = 9/3 b = i/i
a = 3 b = 1

z = a + bi
z = 3 + 1 * i
z = 3 + i

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For the answer to the question above,
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6 0

3 years ago

Read 2 more answers

Simplify 9x - 4 + 3x

rewona [7]

Answer:

$4(3x - 1)$

Step-by-step explanation:

$9x - 4 + 3x$

Adding 9x & 3x gives 12x.

$= > 12x - 4$

Now taking 4 common from both the terms , we get :-

$4(3x - 1)$

3 0

3 years ago

Will give brainliest.

lesya692 [45]

Answer:

1. y = $\frac{-A}{By}$ x + $\frac{C}{By}$

2. Divide the Opposite of A and B

3. Doesn't make sense the y-intercept is C/By sry I can't help that one

Step-by-step explanation:

1. Ax + By = C

By = -Ax + C

y = $\frac{-A}{By}$ x + $\frac{C}{By}$

2. No explanation

3 0

2 years ago

QUICK<br><br> Find the area of the shaded region. Use 3.14 for pi.

ivolga24 [154]

Answer:

The shaded region is $353.25m^2$ .

Step-by-step explanation:

The area of a circle is defined by the multiplication of the square of its radius, or half its diameter, by pi, or simply $A=\pi r^2$ .

15m is the radius of the large circle, and also the diameter of the smaller circles.

The area of the shaded region will be the subtraction of the area of the two smaller circles from the area of the larger circle.

As such:

$A=\pi(15)^{2}-2(\pi(\frac{15}{2} )^{2})\\\\A=(3.14)(15)^{2}-2(3.14)(\frac{15}{2} )^{2}\\A=706.5-353.25\\A=353.25$

4 0

3 years ago

Read 2 more answers

A manufacturer cuts squares from the corners of a rectangular plece of sheet metal that measures 2 inches by 7 inches (see Figur

Vladimir79 [104]

Answer:

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The volume of the open-topped box is equal to

$V=LWH$

where

$L=(7-2x)\ in\\W=(2-2x)\ in\\H=x\ in$

substitute

$V=(7-2x)(2-2x)x$

Convert to expanded form

$V=(7-2x)(2-2x)x\\V=(14-14x-4x+4x^{2})x\\V=14x-14x^2-4x^2+4x^{3}\\V=4x^{3}-18x^{2} +14x$

using a graphing tool

Graph the cubic equation

Remember that

The domain for x is the interval -----> (0,1)

Because

If x>1

then

the width is negative (W=2-2x)

so

The maximum is the point (0.46,3.02)

see the attached figure

therefore

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

8 0

3 years ago