DIVIDING COMPLEX NUMBERS

What is complex number ?

A complex number is the sum of a real number and an imaginary number. A complex number is of the form

a + ib

and its represented by ‘z’.

Write the complex number in standard form :

Example 1 :

2/(3 – i)

Solution :

Given, 2/(3 – i)

Multiply the numerator and denominator by the conjugate of the denominator 3 – i. That is 3 + i

So, the standard form is 3/5 + 1/5i

Example 2 :

(5 + i)/(2 – 3i)

Solution :

Given, (5 + i)/(2 – 3i)

Multiply the numerator and denominator by the conjugate of thedividingcnumbersq2

 denominator 2 - 3i. That is 2 + 3i

So, the standard form is 7/13 + 17/13i

Example 3 :

1/(2 + i)

Solution :

Given, 1/(2 + i)

Multiply the numerator and denominator by the conjugate of the denominator 2 + i. That is 2 – i

So, the standard form is 2/5 - 1/5i

Example 4 :

i/(2 - i)

Solution :

Given, i/(2 - i)

Multiply the numerator and denominator by the conjugate of the denominator 2 - i. That is 2 + i

So, the standard form is -1/5 + 2/5i

Example 5 :

(2 + i)/(2 – i)

Solution :

Given, (2 + i)/(2 – i)

Multiply the numerator and denominator by the conjugate of the denominator 2 - i. That is 2 + i

So, the standard form is 3/5 + 4/5i

Example 6 :

(2 + i)/3i

Solution :

Given, (2 + i)/3i

Multiply the numerator and denominator by the conjugate of the denominator 3i. That is -3i

So, the standard form is 1/3 - 2/3i

Example 7 :

(2 + i)²(-i)/(1 + i)

Solution :

Given, (2 + i)²(-i)/(1 + i)

Multiply the numerator and denominator by the conjugate of the denominator 1 + i. That is 1 – i

(2 + i)²(-i)  =  (4 + i² +4i)(-i)

=  (4-1+4i)(-i)

=  (3+4i)(-i)

=  3i-4i²

=  3i+4

 (3i+4)/(1+i)  =  [(3i+4)/(1+i)] [(1-i)/(1-i)]

=  (-3+7i+4)/(1+1)

=  (1+7i)/2

=  1/2 + (7/2)i

Example 8 :

(2 - i)(1 + 2i)/(5 + 2i)

Solution :

Given, (2 - i)(1 + 2i)/(5 + 2i)

Multiply the numerator and denominator by the conjugate of the denominator 5 + 2i. That is 5 - 2i

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