GMAT GRE 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade 6th Grade 7th grade math 8th grade math 9th grade math 10th grade math 11th grade math 12th grade math Precalculus Worksheets Chapter wise Test MCQ's Math Dictionary Graph Dictionary Multiplicative tables Math Teasers NTSE Chinese Numbers CBSE Sample Papers 
Addition of Complex NumbersAddition of complex numbers : The sum z _{1} + z _{2} of two complex numbers z _{1} = a _{1} + ib _{1} and z _{2} = a _{2} + ib _{2} is defined as the complex number (a _{1} + a _{2} ) + i(b _{1} +b _{2} ), i.ez _{1} + z _{2} = (a _{1} + ib _{1} ) + (a _{2} + ib _{2} ) It is therefore, observed that while adding two complex numbers the real and imaginary parts of the system is obtained by adding the real and imaginary parts of the summands. Examples : 1) (3 + i7) + (4 + i8) = (3 + 4) + i(7 + 8) = 7 + i15 2) (12 i7) + i4 = 12 + i ( 7 + 4) = 12  i3 Properties of addition of complex numbersClosure : The sum of two complex numbers is , by definition , a complex number. Hence, the set of complex numbers is closed under addition.Example : (5+ i2) + 3i = 5 + i(2 + 3) = 5 + i5 < From the above we can see that 5 + i2 is a complex number, i3 is a complex number and the addition of these two numbers is 5 + i5 is again a complex number. Commutative property: For two complex numbers z _{1} = a + ib and z _{2} = c + id z _{1} + z _{2} = (a + ib) +(c +id) = (a + c) + i ( b + d) z _{2} + z _{1} = (c + id) +(a + ib)= (c + a) + i(d + b) But we know that, a + c = c + a and b + d = d + b ∴ z _{1} + z _{2} = z _{2} + z _{1} Associative Property : Consider three complex numbers, z _{1} = a + ib , z _{2} = c + id and z _{3} = e + if (z _{1} + z _{2} )+ z _{3} = z _{1} +(z _{2} + z _{3} ) (a + ib + c + id ) + (e + if) = (a + ib) + ( c +id + e + if) [(a + c) + i( b +d)] + (e + if) = (a + ib) +[(c + e) + i( d +f)] (a + c + e ) + i(b + d + f ) = ( a + c + e) + i(b + d + f) Additive Identity: Let a + ib be the identity for addition. Then (x + iy) + (a + ib) = x + iy ⇒ (x + a) + i( y + b) = x + iy ⇒ x + a = x and y + b = y ⇒ a = 0 and b = 0 Hence, the additive identity is the complex number 0 + i0 , written simply as 0. Additive Inverse: z = a + ib so its additive inverse will be z which (a + ib) =  a  ib 1) Add : 5 + 3i and 8 + 2i Solution : 5 + 3i + (8 + 2i) = ( 5 + (8) + i(3 + 2) =  3 + i5 2) Find the additive inverse of  5 + i7 . Solution : z = 5 + i7 so additive inverse will be z so z =  (z) =  ( 5 + i7) = 5  i7 3) Find the sum of 2/3 + i5/3 ; 2/3i and 5/4  i Solution : Using associative property, we have [( 2/3 + i5/3)+(02/3i)] + (5/4  i) = (2/3 + i) +(5/4  i) = 7/12 From addition of complex numbers to Home
More To Explore
