If prove that x2 + y2 = 1

Q8 of 153 Page 13

If prove that x² + y² = 1

Given:

⇒

We know that for a complex number Z=a+ib it’s magnitude is given by

We know that is

Applying Modulus on both sides we get,

⇒

Squaring on both sides

⇒

⇒ x²+y²=1

∴ Thus Proved.

If z₁ = 2 – i, z₂ = -2 + i, find

ii.

Find the modulus of

Find the least positive integral value of n for which is real.

Find the real values of θ for which the complex number is purely real.