Parts of complex numbers

z = 4- 2i

Step-by-step explanation:

This is the trigonometric form of a complex number where

|

z

|

is the modulus and

θ

is the angle created on the complex plane.

z

=

a

+

b

i

=

|

z

|

(

cos

(

θ

)

+

i

sin

(

θ

)

)

The modulus of a complex number is the distance from the origin on the complex plane.

|

z

|

=

√

a

2

+

b

2

where

z

=

a

+

b

i

Substitute the actual values of

a

=

4

and

b

=

−

2

.

|

z

|

=

√

(

−

2

)

2

+

4

2

Find

|

z

|

.

|

z

|

=

2

√

5

The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.

θ

=

arctan

(

−

2

4

)

Since inverse tangent of

−

2

4

produces an angle in the fourth quadrant, the value of the angle is

−

0.4636476

.

θ

=

−

0.4636476

Substitute the values of

θ

=

−

0.4636476

and

|

z

|

=

2

√

5

.

2

√

5

(

cos

(

−

0.4636476

)

+

i

sin

(

−

0.4636476

)

)

Replace the right side of the equation with the trigonometric form.

z

=

2

√

5

(

cos

(

−

0.4636476

)

+

i

sin

(

−

0.4636476

)

)

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

image result for what is another name for consecutive interior angles? ​

when two lines are crossed by another line (called the transversal): the pairs of angles on one side of the transversal but inside the two lines are called consecutive interior angles. in this example, these are consecutive interior angles: d and f.

step-by-step explanation: