Question

Express each of the following in a+bi form.a)(1+i)²b)(1+i)⁴c)(1+i)⁶

Answer 1

Explanation:

(a)
`\left ( 1+i\right )^2`

`=1+i^2+2i=1-1+2i`

`=0+2i`

(b)
`\left ( 1+i\right )^4`

using above i.e.

`\left ( 1+i\right )^2=2i`

`\left ( 2i\right )\left ( 2i\right )=4i^2`

`=-4+i0`

(c)
`\left ( 1+i\right )^6`

Using above two results

`=\left ( 1+i\right )^2\cdot \left ( 1+i\right )^4`

`=\left ( 2i\right )\left ( -4\right )`

`=-8i`

`=0-8i`