Question

compute the modulus and argument of each complex number. Plot and label each complex number in the complex plane given.


(a) 1 + i

(b) square root3 + i

(c) -2i

(d)-5

(e)5-5i

(f) 7 square root3+7i

(g) −3 + 4i

Answer 1

Given : a) 1 + i

(b) square root3 + i

(c) -2i

(d)-5

(e)5-5i

(f) 7 square root3+7i

(g) −3 + 4i

To Find : compute the modulus and argument of each complex number.

Plot and label each complex number in the complex plane  

Solution:

Z = x +iy  

मापांक   = | Z |  = √x² + y²

कोणांक = tan⁻¹ ( y/x) =  arg(z)

Magnitude (modulus)  =   = | Z |  = √x² + y²

Angle or argument   = tan⁻¹ ( y/x)  =  arg(z)

1 + i

| Z |  = √1² + 1² = √2

arg(z) = tan⁻¹(1/1) =  π/4

√3 + i

| Z |  = √√3² + 1² =  2

arg(z) = tan⁻¹(1/√3) =  π/6

-2i

| Z |  = 2

arg(z)  =   3π/2    or - π/2

-5

| Z |  = 5

arg(z)  =    π

5-5i

| Z |  = 5√2

arg(z)  =   -π/4    or  7π/4

and so on

Learn More:

Geometrically, the modulus of a complex number represents its ...

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Every real number is a complex number. Proof - Brainly.in

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Answer 2

Answer:

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Step-by-step explanation:

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