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3 years ago

Express (5 + 2i) \div (1 - \sqrt{2i)} in a+ib

Mathematics

1 answer:

DochEvi [55]3 years ago

7 0

Answer:

$1 + 2\sqrt{2i}$

Step-by-step explanation:

The expression is presented below:

$= \frac{(5 + \sqrt2i) }{(1 - \sqrt{2i)}}\\\\= \frac{(5 + \sqrt2i) }{(1 - \sqrt{2i)}} \times \frac{1 + \sqrt{2i)}}{1 + \sqrt{2i)}}\\\\= \frac{5 + 5\sqrt{2i} + \sqrt{2i} - 2 }{1 + 2} \\\\= \frac{3 + 6\sqrt{2i} }{3}\\\\= \frac{3(1 + 2\sqrt{2i}) }{3} \\\\= 1 + 2\sqrt{2i}$

The above represents an expression

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I dont know man help please

Ratling [72]

Answer:

m∠1 = 63°

m∠2 = 49°

m∠3 = 87°

m∠4 = 44°

Step-by-step explanation:

From the given figure

∵ ∠2 and 49° are vertically opposite angles

∵ The vertical opposite angles are equal in measures

∴ m∠2 = 49°

∵ The sum of the interior angles of a Δ is 180°

∵ m∠1, m∠2, and 68° are interior angles of a Δ

∴ m∠1 + m∠2 + 68° = 180°

∵ m∠2 = 49°

∴ m∠1 + 49° + 68° = 180°

→ Add the like terms in the left side

∴ m∠1 + 117 = 180

→ Subtract 180 from both sides

∴ m∠1 = 63°

∵ ∠3 and 93° formed a pair of linear angles

∵ The sum of the measures of the linear angles is 180°

∴ m∠3 + 93° = 180°

→ Subtract 93 from both sides

∴ m∠3 = 87°

∵ 93° is an exterior angle of the triangle

∵ The measure of the exterior angle of a Δ at one vertex equals the sum

of the measures of the opposite interior angles to this vertex

∵ ∠4 and 49° are the opposite interior angles to 93°

∴ 49° + m∠4 = 93°

→ Subtract 49 from both sides

∴ m∠4 = 44°

8 0

3 years ago

How do you solve the equation 7^(7n+7)=2,401

RoseWind [281]

7^(7n + 7) = 2401
apply log on both sides to solve the equation
log 7^(7n + 7) = log 2401
the power is brought forward
(7n + 7) log 7 = log 2401
7n +7 = log 2401 / log 7
7n + 7 = 4
7n = -3
n = -3/7

Hope it helped!

5 0

3 years ago

Given that (x+y+z)(xy+xz+yz)=18 and that x^2(y+z)+y^2(x+z)+z^2(x+y)=6 for real numbers x, y, and z, what is the value of xyz?

worty [1.4K]

Answer:

Step-by-step explanation:

$(x+y+z)(xy+xz+yz)=18$ Equation 1

$x^2(y+z)+y^2(x+z)+z^2(x+y)=6$ Equation 2

What is the value of $xyz$ where each variable represents a real number?

Let's expand equation 1:

$(x+y+z)(xy+xz+yz)=18$

$x(xy)+x(xz)+x(yz)+y(xy)+y(xz)+y(yz)+z(xy)+z(xz)+z(yz)=18$

Simplify each term if can:

$x^2y+x^2z+xyz+y^2x+xyz+y^2z+xyz+z^2x+z^2y=18$

See if we can factor a little to get some of the left hand side of equation 2:

The first two terms have $x^2$ and if I factored $x^2$ from first two terms I would have $x^2(y+z)$ which is the first term of left hand side of equation 2.