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photoshop1234 [79]
3 years ago
11

Write the quotient as a +bi 4+6i/ 2-3i​

Mathematics
2 answers:
vladimir1956 [14]3 years ago
4 0

\frac{4+6i}{2-3i}=\frac{(4+6i)(2+3i)}{(2-3i)(2+3i)}

\frac{8+12i+12i+18i^2}{4+6i-6i-9i^2}

\frac{-10+24i}{13}

\boxed{\frac{-10}{13}+\frac{24}{13}i}

Kipish [7]3 years ago
4 0

Answer:

- \frac{10}{13} + \frac{24}{13} i

Step-by-step explanation:

Given

\frac{4+6i}{2-3i}

To rationalise the denominator, multiply the numerator/ denominator by the complex conjugate of the denominator.

The conjugate of 2 - 3i is 2 + 3i, thus

\frac{(4+6i)(2+3i)}{(2-3i)(2+3i)} ← expand factors

= \frac{8+24i+18i^2}{4-9i^2} → i² = - 1

= \frac{8+24i-18}{4+9}

= \frac{-10+24i}{13}

= - \frac{10}{13} + \frac{24}{13} i

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3 years ago
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SOMEBODY PLEASE HELP!! Find the missing value. Show your work please.
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5 0
3 years ago
Value of P: 3/15(p+10)=-15
ArbitrLikvidat [17]
<span>Step  1  :</span> 1 Simplify — 5 <span>Equation at the end of step  1  :</span> 1 (— • (p + 10)) - -15 = 0 5 <span>Step  2  :</span><span>Equation at the end of step  2  :</span> (p + 10) ———————— - -15 = 0 5 <span>Step  3  :</span>Rewriting the whole as an Equivalent Fraction :

<span> 3.1 </span>  Subtracting a whole from a fraction 

Rewrite the whole as a fraction using <span> 5 </span> as the denominator :

-15 -15 • 5 -15 = ——— = ——————— 1 5

<span>Equivalent fraction : </span>The fraction thus generated looks different but has the same value as the whole 

<span>Common denominator : </span>The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

<span> 3.2 </span>      Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(p+10) - (-15 • 5) p + 85 —————————————————— = —————— 5 5 <span>Equation at the end of step  3  :</span> p + 85 —————— = 0 5 <span>Step  4  :</span>When a fraction equals zero :<span><span> 4.1 </span>   When a fraction equals zero ...</span>

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the <span>denominator, </span>Tiger multiplys both sides of the equation by the denominator.

Here's how:

p+85 ———— • 5 = 0 • 5 5

Now, on the left hand side, the <span> 5 </span> cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   p+85  = 0

Solving a Single Variable Equation :

<span> 4.2 </span>     Solve  :    p+85 = 0<span> 

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One solution was found :                  <span> p = -85</span>
7 0
3 years ago
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liberstina [14]
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Given the sequence 7, 12, 17, 22, ...
abruzzese [7]

Answer:

option D is true.

Step-by-step explanation:

Given the sequence

7, 12, 17, 22, ...

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a_n=5\left(n-1\right)+7

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Therefore, option D is true.

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