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Properties of Complex Number Arithmetic

Properties of Complex Number Arithmetic

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 »  Complex Multiplicative inverse of `z` is `1/z`.

    →  `z xx 1/(z) = 1`

Multiplicative Inverse

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  For any complex number `z` there exists `1/z` : multiplicative inverse

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex numbers have multiplicative inverse.


Keep tapping on the content to continue learning.
Starting on learning "Multiplicative Inverse". ;; In this page you will learn about multiplicative inverse of a complex number.

What does 'inverse' mean?

  • same; identical; similar
  • opposite; converse

The answer is 'opposite; converse'.

Consider two complex numbers `z_1 = a+ i b` and `z_2 = 1 /(a+ib)`. What will be `z_1 xx z_2`?

  • `1`
  • `1+0i`
  • multiplicative identity
  • All the above

The answer is 'All the above'

Consider two complex numbers `z_1 = a+ i b` and `z_2 = 1 /(a+ib)`.

`z_2 = 1/(a+ib)`
`quad quad quad = 1/(a+ib) xx (a-ib)/(a-ib) `
`quad quad quad = (a-ib)/(a^2+b^2)`

`1/z` or (a-ib)/(a^2+b^2) is the multiplicative inverse.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Multiplicative Inverse: For any complex number `z = a+ib in CC`, there exists `1/z = (a - i b)/(a^2+b^2) in CC` such that
`z xx 1/z = 1`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

What is the multiplicative inverse of `2-i`?

  • `2+i`
  • `(2+i)/5`
  • `(2+i)/sqrt(5)`

The answer is '`(2+i)/5`'

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What does 'inverse' mean?
same;identical;similar
same; identical; similar
opposite;converse
opposite; converse
The answer is 'opposite; converse'.
Consider two complex numbers z1 = a+ i b and z2 = 1 by a+i b. What will be z1 multiplied z2?
1
1
0
1+0i
multiplicative;identity
multiplicative identity
all;above
All the above
The answer is 'All the above'
Consider two complex numbers z1 = a+ i b and z2 = 1 by a+i b. ;; z2 = 1 by a+i b ;; equals 1 by a+ib into a minus i b by a minus i b ;; equals a minus i b by a squared +b squared ;; 1 by z, or a minus i b by a squared +b squared, is the multiplicative inverse.
For any complex number z there exists 1 by z : multiplicative inverse
Multiplicative Inverse: For any complex number z = a+i b in complex numbers, there exists 1 by z = (a minus i b) by a squared plus b squared in complex numbers such that z into 1 by z equals 1.
What is the multiplicative inverse of 2 minus i?
1
2+i
2
2 plus i, by 5
3
2 plus i, by square root of 5
The answer is 2 plus i, by 5

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