Question

If z=1 +√3i then show
that z²+4=2z​

Answer 1

ANSWER:

Given:

• z = 1 + √3 i

To prove:

• z² + 4 = 2z

Proof:

We are given that,

⇒ z = 1 + √3i

We need to prove that,

⇒ z² + 4 = 2z.

Now, substituting value of z,

⇒ (1 + √3i)² + 4 = 2(1 + √3i)

We know that,

⇒ (a + b)² = a² + b ² + 2ab

So,

⇒ (1 + √3i)² + 4 = 2(1 + √3i)

⇒ (1)² + (√3i)² + 2(1)(√3i) + 4 = 2 + 2√3i

⇒ 1 + 3i² + 2√3i + 4 = 2 + 2√3i

⇒ 5 + 3i² + 2√3i = 2 + 2√3i

We know that,

⇒ i² = -1

So,

⇒ 5 + 3(-1) + 2√3i = 2 + 2√3i

⇒ 5 - 3 + 2√3i = 2 + 2√3i

⇒ 2 + 2√3i = 2 + 2√3i

As, LHS = RHS,

HENCE VERIFIED!!!