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Thought-Process to Discover Knowledge

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User Guide

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nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

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trek,

jogger,

exercise.

User Guide

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User Guide

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summary of this topic

### Properties of Complex Number Arithmetic

Voice

Voice

Home

»  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

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'

Progress

Progress

What does 'inverse' mean?
same;identical;similar
same; identical; similar
opposite;converse
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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