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WINSTONCH [101]
3 years ago
7

Simplify

tyle\frac{1-i}{2+3i}$" alt="$\displaystyle\frac{1-i}{2+3i}$" align="absmiddle" class="latex-formula">, where $i^2 = -1.$
Mathematics
1 answer:
Vlad [161]3 years ago
7 0

Answer:

(-1-5i)/13

Step-by-step explanation:

You can't leave that i on the bottom of the fraction. Thats why it needs work. MULTIPLY the top and the bottom by the CONJUGATE of the bottom term. That means look at the bottom, copy those numbers but make the sign the opposite.

Your question:

(1-i)/(2+3i)

CONJUGATE:

2 - 3i

MULTIPY:

(1-i)/(2+3i) × (2-3i)/(2-3i)

You multiply fractions by multiplying top×top and bottom ×bottom, just straight across.

On top:

(1-i)(2-3i)

2-3i-2i+3i^2

2-3i-2i-3 Note: i^2=-1

-1-5i This goes on top.

On bottom:

(2+3i)(2-3i)

4-6i+6i-9i^2

4-9i^2

4+9

13

final answer:

(-1-5i)/13

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5 0
4 years ago
A park has a 333 meter (\text{m})(m)left parenthesis, start text, m, end text, right parenthesis tall tether ball pole and a 6.8
dybincka [34]

Answer:option B & D are correct

Step-by-step explanation:

Given options are  

                                             A              B          C             D           E        

Tether ball pole shadow      1.35         1.8        3.75        0.6       2

Flagpole shadow                  3.4          4.08      8.35       1.36      4.8

Ratio of corresponding height & shadows  should be same

3 meter tall tether ball pole and a 6.8 tall flagpole

=> Ratio  = 6.8/3    = 68/30  = 34/15  

A    - 3.4/1.35 =   340/135     ≠ 34/15( 306/135)

B  -  4.08/1.8  = 408/180   =  34/15  = 34/15  ( Correct option)

C    8.35/3.75  = 835/375  =  167/75   ≠ 34/15( 170/75)

D  1.36/0.6  = 136/60   =  34/15  = 34/15   ( Correct option)

E  4.8/2  = 48/20   =  12/5   = 36/15    ≠ 34/15

option B & D are correct

6 0
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Step-by-step explanation:

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