The identity property of addition states that any number plus zero equals the original number. So, 6 + 0 = 6 shows the identity property of addition. Other number sentences that show this property would include: 8 + 0 = 8, 153 + 0 = 153, and 1,899,888 + 0 = 1,899,888. In each case, the original number plus 0 equals the original number. It doesn't matter how large or small the original number is.

8 0

3 years ago

What are the fourth roots of 6+6√(3i) ?

Helen [10]

Answer:

Step-by-step explanation:

The genral form of a complex number in rectangular plane is expressed as z = x+iy

In polar coordinate, z =rcos ∅+irsin∅ where;

r is the modulus = √x²+y²

∅ is teh argument = arctan y/x

Given thr complex number z = 6+6√(3)i

r = √6²+(6√3)²

r = √36+108

r = √144

r = 12

∅ = arctan 6√3/6

∅ = arctan √3

∅ = 60°

In polar form, z = 12(cos60°+isin60°)

z = 12(cosπ/3+isinπ/3)

To get the fourth root of the equation, we will use the de moivres theorem; zⁿ = rⁿ(cosn∅+isinn∅)

z^1/4 = 12^1/4(cosπ/12+isinπ/12)

When n = 1;

z1 = 12^1/4(cosπ/3+isinn/3)

z1 = 12^1/4cis(π/3)

when n = 2;

z2 = 12^1/4(cos2π/3+isin2π/3)

z2 = 12^1/4cis(2π/3)

when n = 3;

z2 = 12^1/4(cosπ+isinπ)

z2 = 12^1/4cis(π)

when n = 4;

z2 = 12^1/4(cos4π/3+isin4π/3)

z2 = 12^1/4cis(4π/3)

8 0

3 years ago