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coldgirl [10]
3 years ago
5

please help me The question involves multiplying two complex numbers, then turning it into an a+bi equation (pictures included)

Mathematics
1 answer:
Sloan [31]3 years ago
8 0

Answer:

  (a, b) = (0, -15)

Step-by-step explanation:

In "cis" form the product of two complex numbers is the product of their magnitudes at the angle that is the sum of their angles. I find this the easiest way to multiply complex numbers.

  z1 × z2 = (3 cis π)(5 cis π/2)

  = (3·5) cis (π +π/2)

  = 15 cis 3π/2

Of course, "cis" is short for "cosine + i·sine", so you have ...

  z1 × z2 = 15 cis 3π/2 = 15(cos(3π/2) +i·sin(3π/2))

  = 15(0 +i·(-1))

  = 0 -15i

(a, b) = (0, -15)

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wlad13 [49]

The lengths of the line segments are summarized in the following list:

  1. DF = 3
  2. DE = 8 / 3
  3. FG = 3
  4. FH = 9 / 2
  5. GH = 3 / 2
  6. EH = - 11 / 6
<h3>How to calculate the length of a line segment based on point set on a number line</h3>

Herein we have a number line with five points whose locations are known.  The length of each line segment is equal to the arithmetical difference of the coordinates of the rightmost point and the leftmost point:

DF = - 1 - (- 4)

DF = 3

DE = (- 1 - 1 / 3) - (- 4)

DE = 3 - 1 / 3

DE = 8 / 3

FG = 2 - (- 1)

FG = 3

FH = (3 + 1 / 2) - (- 1)

FH = 4 + 1 / 2

FH = 9 / 2

GH = (3 + 1 / 2) - 2

GH = 1 + 1 / 2

GH = 3 / 2

EH = (3 + 1 / 2) + (- 1 - 1 / 3)

EH = - 2 + (1 / 2 - 1 / 3)

EH = - 2 + 1 / 6

EH = - 11 / 6

To learn more on lengths: brainly.com/question/8552546

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5 0
3 years ago
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Answer:

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Step-by-step explanation:

It is given that the dimensions of rectangle A are four times the dimensions of rectangle B.

Let dimensions of rectangle B are l×b.

So, the dimensions of rectangle A are 4l×4b.

Area of rectangle is

Area=length\times width

Area of rectangle B is

A_B=l\times w

The area of rectangle B is 162 square cm.

A_B=l\times w=162

Area of rectangle A is

A_A=4l\times 4w=16(l\times w)=16(162)=2592

Therefore, the area of rectangle A is 2,592 square cm.

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