True or True

Algebra Level 3

True or False :

If x is a complex number then, $x \times \frac{1}{x}$ is always equal to 1.

True or True

False Not True and Not False True not true and not false

2 solutions

Paul Ryan Longhas
Nov 27, 2014

Since 0 = 0 + 0i ---> 0 is a complex number. If x = 0, then x(1/x) = indeterminate

you mean 0 is a complex number, then 2=2+0i is also a complex number , then each real number is an imaginary number, but i may be wrong , i don't know much about complex numbers

Parv Maurya - 6 years, 6 months ago

All Real numbers are Complex number since Real number is a subset of Complex Number

Paul Ryan Longhas - 6 years, 6 months ago

There is a difference between complex numbers and imaginary numbers. Imaginary numbers are of the form $i \cdot a$ where $a \in \mathbb{R}$ , whereas complex numbers are of the form $a+ib$ where $a,b \in \mathbb{R}$ .

Pratik Shastri - 6 years, 6 months ago

Well actually real numbers are a subset of complex numbers. Your illustration is nice.

Adhiraj Chattopadhyay - 5 years, 11 months ago

Parv Maurya
Nov 29, 2014

substitute x for 1+i , and the answer would be 2 , so the statement is disproved

$\frac1{1+i}=\frac{1-i}2$ $(1+i)\times\frac{1-i}2=\frac22=1$

Kenny Lau - 6 years, 6 months ago

@Kenny Lau .......... really ur soln. is nice ..... i tink the answer shud b TRUE then ..... cud sum1 chek out this??

Ganesh Ayyappan - 6 years, 4 months ago

True or True

2 solutions

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