Explanation

r(cosθ + isinθ)

This is the polar form of a complex number.

where r is the magnitude (or modulus).

θ is the argument (or angle).

Explanation

To find the inverse of 3 in modulo 7, we need to find a number x such that:

3x ≡ 1 (mod 7)

We can try multiplying 3 by each number from 1 to 6:

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9 ≡ 2 (mod 7)

3 × 4 = 12 ≡ 5 (mod 7)

3 × 5 = 15 ≡ 1 (mod 7)

So, the inverse of 3 in modulo 7 is 5.

Explanation

The United States transferred control of the Panama Canal to Panama on December 31, 1999, as per the Torrijos-Carter Treaties.

The canal is currently managed by the Panama Canal Authority, a government-owned entity of Panama.

Explanation

Simply Connected: A region is simply connected if every closed curve within it can be continuously shrunk to a point without leaving the region.

Multi-Connected: A region is multi-connected if it is not simply connected.

This meaning it has "holes" or other topological features that prevent some closed curves from being shrunk to a point within the region.

Explanation

Pulchritude means خوبصورتی

Unsightliness means بدصُورتی

Explanation

u . n = 0, where n is the unit normal to the boundary

This is the impermeability condition, which states that the fluid cannot flow through the fixed boundary.

Explanation

Since ln(x + 3) ≥ 0, we have:

x + 3 ≥ 1 (since ln(u) ≥ 0 when u ≥ 1)

x ≥ -2

Explanation

Explanation

Using Vieta's formulas, we know that α + β = 4/2 = 2 and αβ = 5/2.

Now, α^2β + αβ^2 = αβ(α + β) = (5/2)(2) = 5.

Explanation