Question

Determine two complex numbers, (a+bi) and (c+di), where a and d are irrational numbers and b and c are rational number

Answer 1

`a+ib=√(3)+2i` and
`c+id=3+√(2)i`.

Step-by-step explanation:

Rational number: If a number is defined in the form of p/q, where p and q are integers and q≠0, then it is called a rational number.

For example: 2, 0.2, 3/4 etc.

Irrational number: If a number can not be defined in the form of p/q, where p and q are integers and q≠0, then it is called an irrational number.

For example: √2, 3.222.., π etc.

We need to find two complex numbers, (a+bi) and (c+di), where a and d are irrational numbers and b and c are rational number.

We can choose any irrational numbers for a and d.

`a=√(3),d=√(2)`

We can choose any rational numbers for b and c.

`b=2,c=3`

Two complex numbers are

`a+ib=√(3)+2i`

`c+id=3+√(2)i`

Therefore, the two complex numbers are
`a+ib=√(3)+2i` and
`c+id=3+√(2)i`.

Answer 2

The two complex numbers are
`\sqrt2 + 5i \text{ and } 6 + \sqrt5i`

Step-by-step explanation:

We have to form two complex numbers of the form

`a + ib\\c + id`

such that and d are irrational numbers and b and c are rational numbers.

We know that
`\sqrt2, \sqrt3` are irrational numbers.

5 and 6 are rational numbers.

We put

`a = \sqrt2\\b = 5\\c = 6\\d = \sqrt5\\a+ib = \sqrt2 + 5i\\c + id = 6 + \sqrt5i`

Thus, the two complex numbers are:
`\sqrt2 + 5i \text{ and } 6 + \sqrt5i`