Answer:
-8i
Step-by-step explanation:
To multiply numbers is polar form
z1 = r1 ( cos theta 1 + i sin theta 1)
z2 = r2 ( cos theta 2 + i sin theta 2)
z1*z2 = r1*r2 (cos (theta1+theta2) + i sin (theta1+theta2)
z1 = 2(cos 70° + i sin 70°)
z2 = 4(cos 200+ i sin 200)
z1z2 = 2*4 (cos (70+200) + i sin (70+200)
z1z2 = 8 (cos(270) + i sin (270))
= 8 (0 + i (-1))
=-8i
<h3>
Answers:</h3>
The first ordered pair is ( -4 , -3 )
The second ordered pair is ( 8, 3 )
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Explanation:
The first point is (x,-3) where x is unknown. It pairs up with y = -3 so we can use algebra to find x
x-2y = 2
x-2(-3) = 2 ... replace every y with -3; isolate x
x+6 = 2
x = 2-6
x = -4
The first point is (-4, -3)
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We'll do something similar for the other point. This time we know x but don't know y. Plug x = 8 into the equation and solve for y
x-2y = 2
8-2y = 2
-2y = 2-8
-2y = -6
y = -6/(-2)
y = 3
The second point is (8, 3)
• Increased by 3
n+3
• Twice the number
2(n+3)
• Three times the number
3n
• Final result
2(n+3)-3n
Answer:
y = 
x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 5) ← 2 points on the line
m = 
=
The line crosses the y- axis at (0, 2 ) ⇒ c = 2
y = x + 2 ← equation of line
