Respuesta :
Answer:
The two complex numbers are [tex]\sqrt2 + 5i \text{ and } 6 + \sqrt5i[/tex]
Explanation:
We have to form two complex numbers of the form
[tex]a + ib\\c + id[/tex]
such that and d are irrational numbers and b and c are rational numbers.
We know that [tex]\sqrt2, \sqrt3[/tex] are irrational numbers.
5 and 6 are rational numbers.
We put
[tex]a = \sqrt2\\b = 5\\c = 6\\d = \sqrt5\\a+ib = \sqrt2 + 5i\\c + id = 6 + \sqrt5i[/tex]
Thus, the two complex numbers are: [tex]\sqrt2 + 5i \text{ and } 6 + \sqrt5i[/tex]
Answer:
[tex]a+ib=\sqrt{3}+2i[/tex] and [tex]c+id=3+\sqrt{2}i[/tex].
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.
[tex]a=\sqrt{3},d=\sqrt{2}[/tex]
We can choose any rational numbers for b and c.
[tex]b=2,c=3[/tex]
Two complex numbers are
[tex]a+ib=\sqrt{3}+2i[/tex]
[tex]c+id=3+\sqrt{2}i[/tex]
Therefore, the two complex numbers are [tex]a+ib=\sqrt{3}+2i[/tex] and [tex]c+id=3+\sqrt{2}i[/tex].
