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3 years ago

Write -2i + (9 − 3i) − (6 − 10i) as a complex number in standard form.

Mathematics

2 answers:

vovikov84 [41]3 years ago

8 0

Answer:

5i+3

Step-by-step explanation:

Given the expression

-2i + (9 − 3i) − (6 − 10i)

Where i² = -1 (complex number rule)

Therefore,

-2i + 9-3i-6+10i

Collecting like terms gives

5i+3

Vika [28.1K]3 years ago

6 0

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3 years ago

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Factor the following expression. 36y - 12

Over [174]

Hey there!

36y - 12

FIRST LOOK AT THE GCF (Greatest Common Factor)

36y: 1, 2, 3, 4, 6, 9, 12, 18, 36, and y

12: 1, 2, 3, 4, 6, and 12

GCF: 12

So, 12 would most likely be number before you make your parentheses

12(?y - 1)

The numbers in your original equation both share 3 & -1

So, therefore the factor form of your equation should be: 12(3y - 1)

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2 years ago

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2(h-8)-h=h-16 what is the solution

BartSMP [9]

STEP-BY-STEP SOLUTION:

To solve this equation, first make ( h ) the subject and then simplify as much as possible as displayed below:

2 ( h - 8 ) - h = h - 16

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4 0

3 years ago

F⃗ (x,y)=−yi⃗ +xj⃗ f→(x,y)=−yi→+xj→ and cc is the line segment from point p=(5,0)p=(5,0) to q=(0,2)q=(0,2). (a) find a vector pa

DerKrebs [107]

a. Parameterize $C$ by

$\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath$

with $0\le t\le1$ .

b/c. The line integral of $\vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath$ over $C$ is

$\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt$

$=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt$

$=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt$

$=\displaystyle10\int_0^1\mathrm dt=\boxed{10}$

d. Notice that we can write the line integral as

$\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)$

By Green's theorem, the line integral is equivalent to

$\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy$

where $D$ is the triangle bounded by $C$ , and this integral is simply twice the area of $D$ . $D$ is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.

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3 years ago

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Step-by-step explanation:

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2 years ago