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Thought-Process to Discover Knowledge

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User Guide

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summary of this topic

### Algebra of Complex Numbers

Voice

Voice

Home

Complex Number Division

»  (a+ib) -: (c+id)
by multiplicative identity, multiplicative inverse, distributive properties.

→  = (a+ib)/(c+id) xx (c-id)/(c-id)

→  = ((a+ib)xx(c-id)) / (c^2+d^2)

### Division of complex numbers

plain and simple summary

nub

plain and simple summary

nub

dummy

Division of two complex numbers follows numerical expression laws and properties with i handled as (sqrt(-1))^2 = -1 to arrive at a+bi form.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex numbers division is explained.

Keep tapping on the content to continue learning.
Starting on learning "Division of Complex Numbers". ;; In this page, Complex numbers division is explained.

Consider two complex numbers z_1=a_1+ib_1 and z_2 = a_2+ib_2. What is z_1 / z_2 in a+bi form?

• (a_1a_2+b_1b_2) + i (a_2b_1-a_1b_2)
• a_1/a_2+ib_1/b_2
• ((a_1a_2+b_1b_2)+i(a_2b_1-a_1b_2))/(a_2^2+b_2^2)

The answer is '((a_1a_2+b_1xxb_2)+i(a_2b_1-a_1b_2))/(a_2^2+b_2^2)'

z_1=a_1+ib_1 and z_2 = a_2+ib_2. What is z_1 / z_2?
Solution :
z_3 = z_1 / z_2
quad quad = (a_1+ib_1)/(a_2+ib_2)
quad quad = (a_1+ib_1)/(a_2+ib_2) xx (a_2-ib_2)/(a_2-ib_2)
quad quad = ((a_1+ib_1)xx (a_2-ib_2))/((a_2+ib_2) xx (a_2-ib_2))
quad quad = ((a_1a_2+b_1b_2)+i(a_2b_1-a_1b_2))/(a_2^2+b_2^2)

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Division of two complex numbers : For any complex number z_1=a_1+ib_1 in CC and z_2 = a_2+ib_2 in CC
z_1 / z_2 = ((a_1a_2+b_1b_2)+i(a_2b_1-a_1b_2))/(a_2^2+b_2^2)

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given z_1 = 10+5i and z_2=3-4i what is z_1/z_2?

• (6+8i)/5
• (3i+4)/25
• 10+11i
• (10+11i)/5

The answer is '(10+11i)/5'.

Progress

Progress

Consider two complex numbers z1=a1+i b1 and z2 = a2+i b2. What is z1 / z2 in a+b i form?
1
a1 a2+b1 b2 + i a2 b1 minus a1 b2
2
a1 by a2+i b1 by b2
3
a1 a2+b1 b2+i a2 b1 minus a1 b2 by a2 squared +b2 squared
The answer is a1 a2+b1 b2+i a2 b1 minus a1 b2 by a2 squared +b2 squared
z1=a1+i b1 and z2 = a2+i b2. What is z1 / z2? ;; Solution : ;; z3 = z1 by z2 ;; equals a1+i b1 by a2+i b2 ;; equals a1+i b1 by a2+i b2 multiplied by a2 minus i b2 by a2 minus i b2 ;; equals a1+i b1 multiplied by a2 minus i b2 divided by a2+i b2 multiplied by a2 minus i b2 ;; equals a1 a2+b1 b2+i a2 b1 minus a1 b2 by a2 squared +b2 squared
Division of two complex numbers follows numerical expression laws and properties with i handled as square root of minus 1 whole squared = minus 1, to arrive at a+b i form.
Division of two complex numbers : For any complex number z1=a1+i b1 in complex numbers and z2 = a2+i b2 in complex numbers ;; z1 divided by z2 = a1 a2+b1 b2+i a2 b1 minus a1 b2 by a2 squared + b2 squared
Given z1 = 10+5i and z2=3 minus 4i. what is z1 by z2?
6;8
6_8i by 5
3;3i;
3i+4 by 25
10;11
10+11i
11i by 5
10+11i by 5