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3 years ago

If (3-4i) (x+iy) = 3 root 5 show that x^2 + y^2=9/5

Mathematics

1 answer:

NNADVOKAT [17]3 years ago

5 0

Answer:

the answer is 2 + i.

Step-by-step explanation:

Let the square root of 3 + 4i be x + iy.

So (x + iy) (x +iy) = 3 +4i

=> x^2 + xyi + xyi + i^2*y^2 = 3 + 4i

=> x^2 – y^2 + 2xyi = 3 + 4i

Equate the real and complex terms

=> x^2 - y^2 = 3 and 2xy = 4

2xy = 4

=> xy = 2

=> x = 2/y

Substitute in

=> x^2 - y^2 = 3

=> 4/y^2 - y^2 = 3

=> 4 – y^4 = 3y^2

=> y^4 + 3y^2 – 4 = 0

=> y^4 + 4y^2 – y^2 – 4 =0

=> y^2(y^2 + 4) – 1(y^2 + 4) =0

=> (y^2 – 1) (y^2 + 4) =0

Therefore y^2 = 1, we ignore y^2 = -4 as it gives complex values of y.

Therefore y = 1 and x = 2/1 = 2

The required square root of 3 + 4i is 2 + i.

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Match each circular flower bed on the left to its circumference and its area on the right. Some answer options on the right will

marin [14]

Answer:

Bed A --- Third Option

Bed B --- Fifth Option

Step-by-step explanation:

Flower Bed A)

The formula for circumference is:

$C=2\pi r$

The diameter of A is 10 feet. So, its radius is 5 feet.

Substitute 5 for r. So, the circumference of Bed A is:

$C=2\pi (5)=10\pi\text{ feet}$

The formula for the area of a circle is:

$A=\pi r^2$

Substitute 5 for r:

$A=\pi (5)^2$

Square and simplify:

$A=25\pi \text{ square feet}$

So, the circumference of Bed A is 10π feet and its area is 25π square feet.

Therefore, match Bed A to the third option.

Flower Bed B)

The radius of Bed B is 6 feet. Again, we can use the circumference and area formulas. Substitute 6 for r for circumference:

$C=2\pi (6)$

Multiply:

$C=12\pi\text{ feet}$

Substitute 6 for r for the area formula:

$A=\pi(6)^2$

Square and simplify:

$A=36\pi\text{ square feet}$

So, Bed B has a 12π feet circumference and a 36π square feet area.

Therefore, match Bed B to the fifth option.

And we're done!

8 0

3 years ago

What is an equation for the line with slope 2/3 and 7-intercept 9? 30 points to whoever answers this correctly and gets brainlie

Annette [7]

The equation of the line is y = $\frac{2}{3}$ x + 9

Step-by-step explanation:

The equation of a line in slope-intercept form is y = m x + b, where

m is the slope of the line
b is the y-intercept ⇒ the value of y when x = 0

∵ The line has a slope $\frac{2}{3}$

∴ m = $\frac{2}{3}$

∵ The y-intercept is 9

∴ b = 9

- Substitute the values of m and b in the form of the equation below

∵ y = m x + b

∴ y = $\frac{2}{3}$ x + 9

The equation of the line is y = $\frac{2}{3}$ x + 9

Learn more:

You can learn more about the linear equations in brainly.com/question/12941985

#LearnwithBrainly

4 0

3 years ago

A husband and wife have normal vision, although both of the couple's fathers are red–green color-blind, an inherited X-linked re

Mekhanik [1.2K]

Answer:

1/2

Step-by-step explanation:

Since the recessive gene is carried in the x chromosome and a father can only pass it to a daughter, the father doesn't have the disease nor carries it.

The mother carries the recessive gene because her father passed her his conditioned gene (only having one x chromosome), while her mother gave her a normal one so she can have normal vision.

The chance of having a boy or a girl is 1/2 and the chance of this baby of having both recessive gene is null because in order to have a girl that is color blind both her x chromosomes must have the recessive gene, but the father can't pass it since he doesn't carries it. Therefore the combined probability is 1/2*(1-0) = 1/2.

7 0

3 years ago

Find the coordinates of P so that P partitions AB in the ratio 3:4 with A(-9,-9) and B(5,-2).

ivolga24 [154]

The coordinates of point P are (-3 , -6)

Step-by-step explanation:

If point (x , y) partitions line AB where A = $(x_{1},y_{1})$ and B = $(x_{2},y_{2})$