We'll establish the multiplicative inverse of the given
ratio
is:
(6-3i)/(7+2i)
According to
the rule, it is not allowed that the denominator to be a complex
number.
We'll multiply the ratio by the conjugate of
(7+2i).
The conjugate of 7+2i =
7-2i
(6-3i)/(7+2i) = (6-3i)(7-2i) /
(7+2i)(7-2i)
We'll remove the
brackets:
(6-3i)(7-2i) = 42 - 12i - 21i
- 6
We'll combine the real parts and the imaginary parts
and we'll get:
Now, we'll calculate the difference of
squares:
(7+2i)(7-2i) = (7)^2 - (4i)^2 = 49 + 16 =
65
(6-3i)/(7+2i) = ( 36 -
33i)/65
The multiplicative
inverse of the number
(7+2i)/(6-3i) is:
36/65 -
(33/65)*i
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