Question

(1+i)^-3. Find the value of a and b in the form of a+ib.​

Answer 1

Answer:

_-1_ - _1_i

4. 4

Step-by-step explanation:

(1+i)^-3

__1__ [(a+b)³=a³+b³+3ab(a+b)]

(1+i)³

___1___

1+i³+3i(1+i)

___1___

1+i³+3i+3i² [i³=-i and i²=-1]

___1___

1-i+3i-3

__1__

-2+2i

__1__ × _-2-2i_

-2+2i. -2-2i

_-2-2i_

4-4i²

_-2-2i_

4+4

_-2-2i_

8

_2(-1-i)_

8

_-1-i_

4

_-1_ - _1_i

4. 4