FINDING MODULUS AND ARGUMENT OF A COMPLEX NUMBER WORKSHEET

Problem 1 :

The principal argument of 3/(-1 + i) is

(1) -5𝜋6
(3) -3𝜋4
(2) -2𝜋3
(4) -𝜋2

Solution

Problem 2 :

The principal argument of (sin 40º + i cos 40º)5 is

(1)  -110º    (2)   -70º   (3)   70º   (4)   110º

Solution

Problem 3 :

If (1 + i) (1 + 2i) (1 + 3i) … (1 + ni) = x + iy, then 2 ⋅ 5 ⋅ 10 … (1 + n2) is

(1)1   (2)   i   (3)   x2 + y2    (4)   1 + n2

Solution

Problem 4 :

If ω ≠ 1 is a cubic root of unity (1 + ω)7 = A + Bω, then (A, B) equals

(1)   (1, 0)   (2)   (-1, 1)  (3)   (0,1)   (4)   (1, 1)

Solution

Problem 5 :

The principal argument of the complex number 1 + i324i1 - i3 is
(1) 2𝜋3
(3) 5𝜋6
(2) 𝜋6
(4) 𝜋2

Solution

Answer Key

1)  -3𝜋/4, option (3)

2)  θ = -110º option (1)

3)    x2 + y2 , option (3)   

12 + 12 · 12 + 22 · 12 + 32 ·... 12 + n2 = x2 + y2 1 + 1 · 1 + 4 · 1 + 9 ·... 1 + n2 = x2 + y22 · 5 · 10 ·... 1 + n2 = x2 + y2Squaring on both sides.2 · 5 · 10 .... 1 + n2 = x2 + y2

option (3) is correct.

4)  (A, B) = (1, 1),  option (4)

5)  𝜋/2, option (4)

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