Question

Reduce to the standard form.

Answer 1

The given expression is,

( 1 1−4i − 2 1+i )( 3−4i 5+i )

Lets simplify the above expression,

( 1 1−4i − 2 1+i )( 3−4i 5+i )=( 1 1−4i × 1+4i 1+4i − 2 1+i × 1−i 1−i )( 3−4i 5+i × 5−i 5−i ) =( 1+4i 1−16 i 2 − 2−2i 1− i 2 )( 15−3i−20i+4 i 2 25− i 2 )

By substituting i 2 =−1 , we get

=( 1+4i 17 − 1−i 1 )( 11−23i 26 ) =( −16+21i 17 )( 11−23i 26 ) =( −176+368i+231i−483 i 2 442 ) =( −176+599i+483 442 )

Further simplifying

=( 307+599i 442 )

Thus, the required normal form is 307 442 + 599 442 i .