what is complex number addition and multiplication
The addition of real and imaginary parts of the number is called a complex number
a complex number is the builder of explained math to different group algebra, Trigonometry, set theory
electronic, magnetics field, current measuring, DC and AC, construction building, etc.
basically, complex number in the form of a real number, imaginary number a + bi
if the real part is zero then the resultant value is imaginary
COMPLEX NUMBER ( addition, multiplication )
= 8 + 8 i Where a = 8 is real number b = 8 is also a real
iota is imaginary number
EXAMPLE
if we have two complex number Z1 = ( 5 +8 i ) Z2 = ( 4 +9i )
= 20 +45i + 32i +72 i2
= 20 + 77i + 72 ( -1 )
where i =√ -1 , i² = -1
= 20 - 72 + 77i
a complex number is the builder of explained math to different group algebra, Trigonometry, set theory
electronic, magnetics field, current measuring, DC and AC, construction building, etc.
basically, complex number in the form of a real number, imaginary number a + bi
if the real part is zero then the resultant value is imaginary
if the imaginary part is zero then the resultant value is a real number
complex number diagram is shown below
complex number diagram is shown below
👩
z = a + bi
where a is the real number and b is also a real number
I form imaginary unit number √ -1
can be a value of a = 0 or and b = o
where a is the real number and b is also a real number
I form imaginary unit number √ -1
can be a value of a = 0 or and b = o
then the complex number in the form
EXAMPLE:1
5 + i ( 0 ) = 5 ( result real part of complex number)
EXAMPLE: 2
0 + 6 i = 6 i ( imaginary part of complex no.)
EXAMPLE:3 8 + 9 i = 8 + 9i ( when non zero a and b )
EXAMPLE: 4
9 + √ -9 = 9 + √(-1)9 ( if we solve calculator result infinity)
= 9 + i √ 9 because i = √-1
solve equation problem in math describe sign i
COMPLEX NUMBER ( addition, multiplication )
if we have two complex number z1 = (x1 ,y1 ) = x1+iy1
z2 = ( x1, y2) = x2 + iy2
(1) ADDITION
z1+z2 = (x1 , y1 ) + ( x1 , y2)
= x1 + iy1 + x2 + iy2
= ( x1 + x2 ) + i ( y1 + y2 )
EXAMPLE
z1 = 6 + 7i , z2 = 8 + 9i
= x1 + iy1 + x2 + iy2
= ( x1 + x2 ) + i ( y1 + y2 )
EXAMPLE
z1 = 6 + 7i , z2 = 8 + 9i
z1+z2 = ( x1 + x2 ) + i ( y1 + y2 )
= ( 6 +8 ) + i ( 7 + 9 )
= ( 14 , 16 )
= ( 6 +8 ) + i ( 7 + 9 )
= ( 14 , 16 )
( 2 ) MULTIPLICATION
a complex number can be multiplied by any number a +bi we multiply simply any number ( natural, whole, integer, real, rational, irrational, real number ) with a complex number
= 8 + 8 i Where a = 8 is real number b = 8 is also a real
iota is imaginary number
EXAMPLE
if we have two complex number Z1 = ( 5 +8 i ) Z2 = ( 4 +9i )
Z1 *Z2 = ( 5 +8i ) * ( 4 + 9i )
= 20 +45i + 32i +72 i2
= 20 + 77i + 72 ( -1 )
where i =√ -1 , i² = -1
= 20 - 72 + 77i
= -52 + 77 i
SOLVE SOME QUESTION TO PRACTICE 0f ( addition and multiplication )
Q. 1
Q. 1
Z = 3 ( 8 - 4 i )
Z =?
A = 24 -12i
B= 24 + 12i
C = 10 - 12i ( answer in comment box )
Q.2
Z1*Z2 =?
Z =?
A = 24 -12i
B= 24 + 12i
C = 10 - 12i ( answer in comment box )
Q.2
Z1 = ( 7 - 2i ) , Z2 = ( 1 + 9i )
Z1*Z2 =?
A = 20 +61 i
B = 25 + 61 i
C = 7 + 18 i ( answer in comment box )
Q .3
if Z1 = ( 0 + 9i ) , Z2 = ( 6 +0i )
Z1 + Z2 = ?
A = 0 + 6 i
A = 0 + 6 i
B = 6 + 0i
C = 6 + 9i ( answer in comment box )
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