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Bezzdna [24]
3 years ago
7

Write the expression 2i^15-i^7 in the standard form a + bi

Mathematics
1 answer:
elixir [45]3 years ago
7 0
\bf 2i^{15}-i^7\qquad 
\begin{cases}
i^2=\sqrt{-1}\cdot \sqrt{-1}\implies \sqrt{(-1)^2}\implies -1\\\\
i^4=i^2\cdot i^2\implies -1\cdot -1\implies 1
\end{cases}\\\\
-----------------------------\\\\
2i^{4+4+4+2+1}-i^{4+2+1}\implies 2i^4i^4i^4i^2i^1-i^4i^2i^1
\\\\\\
(2\cdot 1\cdot 1\cdot 1\cdot -1\cdot i)-(1\cdot -1\cdot i)\implies -2i-(-i)
\\\\\\
-2i+i\implies -i\implies \boxed{0-i}
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The edges of the diameter of a circle are at (-1,2) and (3,-1). Write the equation of the circle in general form.
Y_Kistochka [10]

Answer:

(x-1)²+ (y-0.5)²=6.25

Step-by-step explanation:

<u>The standard form of equation of a circle is;</u>

(x-a)²+(y-b)²=r² where (a,b) are the center of the circle and r is the radius

<u>Finding the mid-point of the given points</u>

(-1,2) and (3,-1)⇒midpoint will be 1/2(x₁+x₂) , 1/2(y₁+y₂)

midpoint= {1/2(-1+3), 1/2(2+-1)}

midpoint=(1,0.5)

<u>Finding the radius r; the distance from the center to either of the given two points</u>

Apply the distance formula d=√ (x₂-x₁)² +(y₂-y₁)²

Taking (x₁,y₁) as (1,0.5) and (x₂,y₂) as (-1,2) then

d=√ (-1-1)² +(2-0.5)²

d= √ (-2)²+(1.5)²

d=√4+2.25⇒√6.25⇒2.5

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<u>Equation of the circle</u>

(x-1)² + (y-0.5)²=2.5²

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Step-by-step explanation:

3 0
3 years ago
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True or false : <br> 20÷4x5= 1<br> 10+10÷2=15<br> 6+4×5=50<br> 12_3×2=6<br> 81÷9+2=11
ELEN [110]
To solve, you must use order of operations. The acronym used is BEDMAS (brackets, exponents, division/multiplication, addition/subtraction), which is the order you solve in. 

F  20÷4x5
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    =25
      
T   10+10÷2
      =10+5
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F    6+4×5
      =6+20
      =26

<span>T   81÷9+2
     =9+2
     =11</span>
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