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Division of Complex Number
by Apolinario "Sam" Ortega, founder IN-V-BAT-AI


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Division of Complex Number





Sequence #1. Multiply the numerator by conjugate.

( + j ) ( + j ) conjugate

Student should already master binomial multiplication.

Binomial multiplication means taking two expressions with two terms each and ensuring that every term in the first binomial multiplies every term in the second. This is just the distributive property applied twice.

For any binomials: 

(3 + j4)(2 + j5)

Multiply each term: 

= 3*2 + 3*j5 + j4*2 + j4*j5

Then combine like terms.

FOIL is simply a memory aid for the four products created when multiplying two binomials:



(3 + j4)(2 + j5) 
First:  3*2   = 6
Outer:  3*j5   = j15
Inner:  j4*2   = j8
Last:   j4*j5   = j220

Combine: 6 + j23 + j220
j = √ -1 j 2 = (-1) (1 / 2)* 2 j 2 = - 1

Simplify: 6 + j23 + (j2 = -1) 20
Simplify: 6 + j23 + (-1)*20
Simplify: 6 + j23 - 20
Simplify: -14 + j23

Binomial multiplication is just the distributive property: 

(a + b)(c + d)
= a(c + d) + b(c + d)
= ac + ad + bc + bd

You are ensuring that every term interacts with every other term, producing a complete expansion.

+ j + j 2 = NUMERATOR

Numerator after simplifying the constant = + j



IF THERE IS NO IMAGINARY NUMBER J = 0 ;
For example
100 / 2 - j 5 becomes
100 - j 0 / 2 - j 5

( + j ) ( + j ) conjugate

After simplification:

+ j + j 2 = DENOMINATOR

After simplification: 4 + ( -25 * - 1)
= 4 + 25 = 29

Denominator = Modulus of w =



Memory recall lesson learned about multiplication of exponent rule

j = √ -1 j 2 = (-1) (1 / 2)* 2 j 2 = - 1

Numerator = -14 + j23
Denominator = Modulus = 29

-14/29 = -0.4828 real number part

and the imaginary part j 23/29 = j 0.7931


+ j
ANSWER IN COMPLEX NUMBER

∠
ANSWER IN POLAR

e J
ANSWER IN EXPONENTIAL



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