COMPLEX NUMBER
A complex number is an expression of the form as follows:
𝒁 = 𝜶 + 𝒊𝜷
Where α and β are real numbers, is called the real part of Z and is denoted by Re Z. β is
called the imaginary part of z and is denoted by Im z. Sometimes the representation of the
form shown is called the Cartesian or rectangular form of the complex number z. Complex
numbers can be added and multiplied using the normal rules of algebra.
EXAMPLE
Let Z=2+3i and W=5-4i. Calculate:
1) Z + W
2) 3W - 5Z
3) ZW
To solve the first one, it would be as follows:
𝒁 + 𝑾 = (2 + 3𝑖) + (5 − 4𝑖) =
2 + 3𝑖 + 5 − 4𝑖 =
𝟕−𝒊
To solve the second one, it would be as follows:
𝟑𝑾 − 𝟓𝒁 = 3(5 − 4𝑖) − 5(2 + 3𝑖) =
(15 − 12𝑖) − (10 + 15𝑖) =
15 − 12𝑖 − 10 − 15𝑖 =
𝟓 − 𝟐𝟕𝒊
To solve the third one, it would be as follows:
𝒁𝑾 = (2 + 3𝑖)(5 − 4𝑖) =
𝒁𝑾 = (2 + 3𝑖)(5 − 4𝑖) =
(2(5) + 2(−4𝑖)) + (3𝑖(5) + 3𝑖(−4𝑖)) =
10 − 8𝑖 + 15𝑖 − 12𝑖 2 =
𝟏𝟎 + 𝟕𝒊 − 𝟏𝟐𝒊𝟐
A complex number is an expression of the form as follows:
𝒁 = 𝜶 + 𝒊𝜷
Where α and β are real numbers, is called the real part of Z and is denoted by Re Z. β is
called the imaginary part of z and is denoted by Im z. Sometimes the representation of the
form shown is called the Cartesian or rectangular form of the complex number z. Complex
numbers can be added and multiplied using the normal rules of algebra.
EXAMPLE
Let Z=2+3i and W=5-4i. Calculate:
1) Z + W
2) 3W - 5Z
3) ZW
To solve the first one, it would be as follows:
𝒁 + 𝑾 = (2 + 3𝑖) + (5 − 4𝑖) =
2 + 3𝑖 + 5 − 4𝑖 =
𝟕−𝒊
To solve the second one, it would be as follows:
𝟑𝑾 − 𝟓𝒁 = 3(5 − 4𝑖) − 5(2 + 3𝑖) =
(15 − 12𝑖) − (10 + 15𝑖) =
15 − 12𝑖 − 10 − 15𝑖 =
𝟓 − 𝟐𝟕𝒊
To solve the third one, it would be as follows:
𝒁𝑾 = (2 + 3𝑖)(5 − 4𝑖) =
𝒁𝑾 = (2 + 3𝑖)(5 − 4𝑖) =
(2(5) + 2(−4𝑖)) + (3𝑖(5) + 3𝑖(−4𝑖)) =
10 − 8𝑖 + 15𝑖 − 12𝑖 2 =
𝟏𝟎 + 𝟕𝒊 − 𝟏𝟐𝒊𝟐
