Math Assignment Help With Operations On Complex Numbers

1.4 Operations on Complex Numbers

1.4.1 Sum of a complex number: For any complex number z1 = a+ib and z2 = c + id

z1 + z2 = (a + ib) + (c + id)

z1 + z2 = (a + c) + i( b + d)

1.4.2 Difference of complex number : For any complex number z1 = a+ib and z2 = c + id

z1 - z2 = (a + ib) - (c + id)

z1 - z2 = (a - c) + i( b - d)

1.4.3 Product of a complex number : For any complex number z1 = a+ib and z2 = c + id

z1 z2 = (a + ib) (c + id)

z1 z2 = (ac - bd) + i( ad + bc)

1.4.3.1 Multiplying a complex number by a real number. In the above formula for multiplication, if d is zero, then we get the formula for multiplying a complex number a+ib and a real number c together:

(a + bi) c = ac + bc i

1.4.3.2 Multiplying a complex number by i. In finding a geometric interpretation of complex multiplication, consider multiplication by an arbitrary complex number z = a + ib by i.

z i = (a + ib) i = –b + ai.

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