# Multiplication and division method of a complex numbers

When the addition and subtraction method of a complex numbers must be in rectangular form,

__the multiplication and division method of a complex numbers__, should be in polar form. Where has the rule:

*absolute*value multiplied (or divided) with

*absolute*value. For

*angle*value have rules: if multiplication,

*angle*value added with

*angle*value and if division,

*angle*value subtracted with

*angle*value.

Sample question 1: (36 ∠ 22°) × (5 ∠ 45°) = ?

Completion:

r (

φ (

Result:

(36 ∠ 22°) × (5 ∠ 45°) = 180 ∠ 67°

If there is a question multiplication (or division) of rectangular and polar, then the rectangular form must be converted into polar form.

Sample question 2: (14 +

Completion:

Conversion rectangular form (14 +

14 +

we have

r (

φ (

Result:

(14 +

Completion:

r (

*abs*) = 36 × 5 = 180φ (

*angle*) = 22 + 45 = 67Result:

(36 ∠ 22°) × (5 ∠ 45°) = 180 ∠ 67°

If there is a question multiplication (or division) of rectangular and polar, then the rectangular form must be converted into polar form.

Sample question 2: (14 +

*j*63) ÷ (25 ∠ 37°) = ?Completion:

Conversion rectangular form (14 +

*j*63) into polar form14 +

*j*63 = 64.53681 ∠ 77.47119°we have

r (

*abs*) = 64.53681 ÷ 25 = 2.58147φ (

*angle*) = 77.47119 - 37 = 40.47119Result:

(14 +

*j*63) ÷ (25 ∠ 37°) = 2.58147 ∠ 40.47119°

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