ANSWER: 8/21
Step:
1. Find the GCF (Greatest Common Factor)
The two denominator which is the bottom number have to be the same ALWAYS when adding and subtracting the fraction. So to find the GCF, you keep multiplying until you see the same number, only use the bottom number to find the GCF
7: 7, 14, 21, 28
3: 3, 6, 9, 12, 15, 18, 21, 24, 27
GCF= 21
2. 5/7 -1/3
Multiple both to get 21
5/7 x 3/3 = 15/21
1/3 x 7/7 = 7/21
3. Sove
15/21 - 7/21
= 8/21
<h3>
Answer: 16</h3>
Work Shown:
range = max - min = 10 - (-6) = 10 + 6 = 16
The range is the distance from the smallest item to the largest. Use of a number line might help sort out the values to see which is the smallest and largest.
Answer:
128 miles
Step-by-step explanation:
5 + 3 = 8, 32 / 8 = 4, 4 x 4 = 16
5 x 16 = 80
3 x 16 = 48
80 + 48 = 128
Answer:
You will obtain a complex number rotated by an angle of 45 degrees (counterclockwise) with a modulus scaled by √2
Step-by-step explanation:
In order to see the effect of multiplying z by 1 + i, you can use the representation of complex numbers in the <em>Polar Form</em>. This representation gives you the angle formed by the complex number and the real axis and the distance from the origin to the point.
Let z=a+ib represent a complex number.<em> The Polar</em> Form is:
z = |z| (Cosα + iSinα)
Where |z| is the modulus of the complex number and α is the angle formed with the real axis.
|z| = √a²+b²
α= arctan (b/a)
The multiplication in<em> Polar Form</em> is:
Let Z0 and Z1 represent two complex numbers
Z0= |Z0| (Cosα + iSinα)
z1= |z1|(Cosβ + iSinβ)
The multiplication is:
Z0.Z1 = |Z0||Z1| [Cos(α+β) + i Sin(α+β)]
Notice that when you multiply complex numbers, you are adding angles and multiplying modulus. The addition of angles can be seen as a rotation of the complex number on the plane and the multiplication of modulus can be seen as changing the modulus of the complex number.
The given number 1+i in the Polar Form is:
z = |z| (Cosα + i Sinα)
|z| = √1²+1² = √2
α = arctan(1/1) = 45°
Therefore, you will obtain a complex number rotated by an angle of 45 degrees with a modulus scaled by √2
