**Question:**

If , then

equals

(a) -1

(b) 1

(c) -i

(d) i

**Solution.**

Using De Moivre’s theorem,

which in turn equals

Hence, .

More complex stuff to be continued in next blog (pun intended) ðŸ™‚

Nalin Pithwa

Mathematics demystified

July 28, 2015 – 11:23 pm

**Question:**

If , then

equals

(a) -1

(b) 1

(c) -i

(d) i

**Solution.**

Using De Moivre’s theorem,

which in turn equals

Hence, .

More complex stuff to be continued in next blog (pun intended) ðŸ™‚

Nalin Pithwa

July 23, 2015 – 11:06 am

**Problem.**

Let ABC be a triangle and be the altitude through A. Prove that

.

(As usual, a, b, c denote the sides BC, CA, AB respectively.)

**Proof.**

The given inequality is equivalent to .

where is the area of triangle ABC. Using the identity

, we see that the inequality to be proved is

(here we use ), which is true. Observe that equality holds iff . QED.

More later,

Nalin Pithwa