Question

(5) Amplitute of argument z = 1+i is
(a)60 degree
(b) 30degree
(c) 90degree
(d) 45°​

Answer 1

Answer:

30°

Step-by-step explanation:

(5) Amplitute of argument z = 1+i is

(b) 30degree

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Answer 2

Given ,

The complex number is z = 1 + i

On comparing z with rcosΦ + irsinΦ

1 = rcosΦ --- (i)

1 = rsinΦ --- (ii)

Squaring eq (i) and eq (ii) , we get

1 = r²cos²Φ --- (iii)

1 = r²sin²Φ --- (iv)

Adding eq (iii) and eq (iv) , we get

1 + 1 = r²cos²Φ + r²sin²Φ

2 = r²(cos²Φ + sin²Φ)

2 = r²(1)

r = √2

Put r = √2 in eq (i) , we get

1 = √2cosΦ

cosΦ = 1/√2

cosΦ = cos(45)

Φ = 45

$\therefore$ The argument or amplitude of given complex number is 45°