A painter is going to paint the rooms of a building. The painter has used 80 gallons of paint and has painted 32% of the rooms.
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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.
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
Then we will multiply both sides of the equation by 2 π :
x + π ( 1 - x ) = 0
x + π - π x = 0
x ( 1 - π ) = - π / · ( - 1 )
x ( π - 1 ) = π
x = π / ( π - 1 )
