Given:⇒ (1+i)z=(1-i)Dividing with (1+i) on both sides we get,⇒ ⇒ ⇒ We know that i2=-1⇒ ⇒ ⇒ ⇒ z=-i∴ Thus proved

Q18 of 153 Page 13

If then show that

Given:

⇒ (1+i)z=(1-i)

Dividing with (1+i) on both sides we get,

⇒

We know that i²=-1

⇒

⇒ z=-i

∴ Thus proved

Evaluate the following :

2x4 + 5x3 + 7x2 – x + 41, when x = - 2 - √3i

For a positive integer n, find the value of

Solve the system of equations Re(z²) = 0, |z| = 2.

If is purely imaginary number (z ≠ – 1), find the value of |z|.