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Evgesh-ka [11]
3 years ago
5

Now examine |a + bi| and complete the definition below. The absolute value of any complex number a + bi is the from (a, b) to (0

, 0) in the complex plane.

Mathematics
2 answers:
sergejj [24]3 years ago
8 0
Distance

|a+bi| is the length of the vector from origin to (a,b).

|a+bi| = \sqrt{a^2 + b^2}
julsineya [31]3 years ago
4 0

Answer:

\sqrt{a^2+b^2} which is the absolute value of complex plane |a+ib|

Step-by-step explanation:

The absolute value of any complex number is its modulus for which we have a formula of modulus

\sqrt{a^2+b^2} where a and b are real numbers.

Please look at the attachement for complex plane of the given points (a,b) and (0,0)

The distance between two points (x_1,y_1) and (x_2,y_2)] will be

\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Here we need to find the distance between (a,b) and (0,0)

on substituting the values in distance formula we will get

\sqrt{(0-a)^2+(0-b)^2}

\Rightarrow\sqrt{a^2+b^2} which is the absolute value of complex plane |a+ib|

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sweet-ann [11.9K]

Answer:

x = 10\sqrt{3}, y = 10

Step-by-step explanation:

Using the sine/ cosine ratios in the right triangle and the exact values

sin60° = \frac{\sqrt{3} }{2} , cos60° = \frac{1}{2} , then

sin60° = \frac{opposite}{hypotenuse} = \frac{x}{20} = \frac{\sqrt{3} }{2} ( cross- multiply )

2x = 20\sqrt{3} ( divide both sides by 2 )

x = 10\sqrt{3}

and

cos60° = \frac{adjacent}{hypotenuse} = \frac{y}{20} = \frac{1}{2} ( cross- multiply )

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y = 10

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3 years ago
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3 years ago
One canned juice drink is 20% orange juice; another is 10% orange juice l. How many liters of each should be mixed together in o
Anni [7]

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Step-by-step explanation:

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3 years ago
Please help! please show the work and not give me and answer thank you ❤️
Citrus2011 [14]

Ans. 1 Angle E and angle F are corresponding angles.

Solution 2.

So,

angle E = angle F

=> x + 20 = 5x - 20

=> x + 20 + 20 = 5x

=> x + 40 = 5x

=> 40 = 5x - x

=> 40 = 4x

=> 40/4 = x

=> 10 = x

Solution 3.

E = x + 20

=> E = 10 + 20

=> E = 30

F = 5x - 20

=> F = 5(10) - 20

=> F = 50 - 20

=> F = 30

<em>Again</em><em> </em><em>justified</em><em> </em><em>that </em><em>they </em><em>are </em><em>equal</em><em> (</em><em> </em><em>besides</em><em> </em><em>answer </em><em>1</em><em>)</em><em>.</em>

8 0
3 years ago
In circle O, what is mArc A E?
posledela

Answer:

Option (3). 120° will be the answer.

Step-by-step explanation:

By using the theorem of secants intersecting externally,

Measure of angle formed by two secants, from a point outside the circle is half the difference of the measures of the intercepted arcs.

m∠C = \frac{1}{2}(m\widehat{AE}-m\widehat{BD})

36° = \frac{1}{2}(m\widehat{AE}-48)

72° = m\widehat{AE}-48°

m\widehat{AE} = 72 + 48

m\widehat{AE} = 120°

Therefore, Option (3) is the answer.

7 0
3 years ago
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