Question

Evaluate these complex
numbers: (40∟ 50° + 20∟− 30°).​

Answer 1

Answer:

80L

Step-by-step explanation:

40L+50+20L-30

40L+50=90L+20L=110-30=80

Answer 2

Concept

A complex number is created by adding a real and an imaginary number together. Complex numbers have the formula a + ib and are typically symbolised by the symbol z. Here, both the numbers a and b are real. The value 'a' is known as the real component and is indicated by Re(z), while 'b' is known as the imaginary part and is denoted by Im (z). Also known as an imaginary number, 'ib'.

Given

the complex numbers are: (40∠50° + 20∠− 30°)

using polar to rectangular formation.

40∠50° = 40( cos 50° ₊ j sin 50°)

= (40×0.6427) ₊ ( 40 × j 0.7660)

= 25.71 ₊ j  30.64

20∠− 30° = 20( cos ₋30° ₊ j sin ₋30°)

= (20×0.8660) ₊ ( 20 × j (₋0.5))

= 17.32 ₋ j 10

adding both the complex numbers.

40∠50° + 20∠− 30° = 25.71 ₊ j  30.64 ₊  17.32 ₋ j 10

= 43.03+j 20.64

converting it to complex number.

47.72 ∠ 25.63°

take the square root of it.

(40∠50° + 20∠− 30°)¹/² = 6.91∠12.81°

hence after evaluating the complex numbers we get the answer as

6.91∠12.81°

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