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 (abs) = 36 × 5 = 180

φ (angle) = 22 + 45 = 67

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 + j63) ÷ (25 ∠ 37°) = ?

Completion:

Conversion rectangular form (14 + j63) into polar form

14 + j63 = 64.53681 ∠ 77.47119°

we have

r (abs) = 64.53681 ÷ 25 = 2.58147

φ (angle) = 77.47119 - 37 = 40.47119

Result:

(14 + j63) ÷ (25 ∠ 37°) = 2.58147 ∠ 40.47119°
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