Q1 of 153 Page 13

Express the following complex numbers in the standard form a + i b :
(1 + i) (1 + 2i)

Given:

⇒ a+ib = (1+i)(1+2i)

⇒ a+ib = 1(1+2i)+i(1+2i)

⇒ a+ib = 1+2i+i+2i²

We know that i²=-1

⇒ a+ib = 1+3i+2(-1)

⇒ a+ib = 1+3i-2

⇒ a+ib=-1+3i

∴ The values of a, b are -1, 3.

Find the value of following expression:

1 + i² + i⁴ + i⁶ + i⁸ + ... + i²⁰

Find the value of following expression:

(1 + i)⁶ + (1 – i)³

Express the following complex numbers in the standard form a + i b :

Express the following complex numbers in the standard form a + i b :(1 + i) (1 + 2i)