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stiks02 [169]
3 years ago
12

Simplify the expression 2+3i/4+3i Please help

Mathematics
1 answer:
rjkz [21]3 years ago
7 0

Answer:

17+6i

-----------

25

Step-by-step explanation:

2+3i

---------

4+3i


We want to multiply by the complex conjugate of the denominator

4+3i has a complex conjugate of 4-3i

2+3i             4-3i

--------- * --------------

4+3i           4-3i


Lets multiply the numerator

(2+3i) ( 4-3i)

2*4 +4*3i -3i*2 - 3i*3i =

8 +12i -6i - 9i^2

Remember i^2 = -1

8 +6i -9(-1)

17 +6i


Lets multiply the denominator

(4+3i) ( 4-3i)

4*4 +4*3i -3i*4 - 3i*3i =

16 +12i -12i - 9i^2

Remember i^2 = -1

16 -9(-1)

25

Putting numerator over denominator

17+6i

-----------

25

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Take the logarithm of both sides. The base of the logarithm doesn't matter.

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Move the terms containing <em>x</em> to the left side and factor out <em>x</em> :

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Solve for <em>x</em> by dividing boths ides by 5 log(4) - log(3) :

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You can stop there, or continue simplifying the solution by using properties of logarithms:

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You can condense the solution further using the change-of-base identity,

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