complex numbers

Question

The Number System is built in stages to facilitate the four basic operations. It is extended to complex numbers to facilitate the computation of square roots of negative real numbers. All you need to remember to work with complex numbers is that they work exactly like algebraic expressions of the form a+bi where a and b are real numbers, except that

1^2=-1 

There is a trick related to dividing complex numbers: you multiply numerator and denominator with the conjugate complex of the denominator. This makes the denominator real, and the standard form of the complex number follows from the distributive law. Express the complex fraction below in standard form. Remember that the real or the imaginary part may be negative.

(1-3i)/(2+i)= 

what is the standard form?

Answer 1

(1-3i)/(2+i)=(1-3i)(2-i)/((2+i)(2-i)=(-1-7i)/5=-1/5-7i/5

Answer 2

 4th line : i^2 = - 1

 

( 1 - 3i) /( 2 + i  ) = (1 - 3i ) / ( 2 + i)

 

( 1 - 3 i) / ( 2 - i) / ( 2 - i) ( 2 + i ) =

 

 ( 2 - 3i - i - 3 ) / ( 4 + 1)=

 

   - 1/5 -4/5i

 

Standard form of the complex numbers are  a + bi, where real and imaginary part are separated.