Explanation

z-3| + |z+3| = 8 = sum of distances from points 3 and -3 = 8

Distance between foci = |3 - (-3)| = 6

Rule: sum > distance between foci → Ellipse  

Here 8 > 6 → condition satisfied

So it’s an ellipse with foci at 3 and -3.

Last verified on 04-06-2026

Explanation

1. AB is one side → D = A + C - B = (-1+1-6, 2-20-2) = (-6, -20)
2. AC is one side → D = A + B - C = (-1+6-1, 2+2+20) = (4, 24)
3. BC is one side → D = B + C - A = (6+1+1, 2-20-2) = (8, -20)

Explanation

(1 + i)¹⁰ = (√2)¹⁰ × [cos(45°×10) + i sin(45°×10)]

           = 2⁵ × [cos450° + i sin450°]

           = 32 × [cos90° + i sin90°] 450° = 360° + 90°

           = 32 × [0 + i×1]

           = 32i

Last verified on 04-06-2026

Explanation

The Fourier series expansion of an even, periodic function contains only cosine terms and a constant term.

In other words, the sine terms are absent.

Even functions:

An even function is symmetric about the y-axis, meaning f(x) = f(-x). 

Fourier series:

A Fourier series represents a periodic function as a sum of sine and cosine waves. 

Explanation