Answer:
Step-by-step explanation:
A complex number is defined as z = a + bi. Since the complex number also represents right triangle whenever forms a vector at (a,b). Hence, a = rcosθ and b = rsinθ where r is radius (sometimes is written as <em>|z|).</em>
Substitute a = rcosθ and b = rsinθ in which the equation be z = rcosθ + irsinθ.
Factor r-term and we finally have z = r(cosθ + isinθ). How fortunately, the polar coordinate is defined as (r, θ) coordinate and therefore we can say that r = 4 and θ = -π/4. Substitute the values in the equation.
![\displaystyle \large{z=4[\cos (-\frac{\pi}{4}) + i\sin (-\frac{\pi}{4})]}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7Bz%3D4%5B%5Ccos%20%28-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%20%2B%20i%5Csin%20%28-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5D%7D)
Evaluate the values. Keep in mind that both cos(-π/4) is cos(-45°) which is √2/2 and sin(-π/4) is sin(-45°) which is -√2/2 as accorded to unit circle.
Hence, the complex number that has polar coordinate of (4,-45°) is
So if it has to be simplified, there is only one answer if all of it is positive but it has a solution to do with minus numbers which is -2 (-x-2)
<h3>
Answer: 12 square units</h3>
Explanation:
Rectangle ABDE is 4 units across the horizontal, and 2 units tall.
The area of this rectangle is length*width = 4*2 = 8 square units.
Triangle BCD has a base of 4 and height 2. The area of which is base*height/2 = 4*2/2 = 4 square units.
The total area is
rectangle + triangle = 8 + 4 = 12 square units
There are 12 wheels on 4 tricycles.
Step-by-step explanation:
Before we answer, the area of a Circle given it radius is
The area of a circle given it diameter is
So let answers question 1-4.
1. The area is
2. The area is
3.
4.
For the 5th problem, circumference is
where d is the diameter and
where r is the radius.
A circumference of 100 m means the radius is 50 because
So this means the area is
