Question

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

Answer 1

Answer:

Step-by-step 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

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

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

$=-8i$

$=0-8i$