## Example 1.2.14 (c): Multiplying geometrically |

Find both geometrically and algebraically and confirm that both answers agree. |

Working algebraically with rectangular coordinates we get:

To work geometrically we need to find length and angle of the vectors involved:

|1/(1+i)| = 1andArg(1+i) = arctan(1) = /4

since *1+i* and *c(1+i)* have the same argument for
any real number *c > 0*. Similarly

|1/2(1+i)| = 1andArg(1+i) = arctan() = /3

Thus, by our theorem about dividing geometrically, we have:

= 1/1*cis(/4-/3) = cis(-/12) = 0.9659258263 - 0.2588190451 i

Therefore, both ways give the same answer.