Question

SAT subject test problem:
What is the reciprocal of 8-3i?

Answer 1

1/(8-3i)

Answer 2

that is not one of the answer choices.
here are the choices:
a) 1/8
b)8+3i/55
c)8-3i/55
d)8+3i/73
e)1/11

Answer 3

@tomo sorry, could you see if you could do this one also?

Answer 4

reciprocal of i is -i

Answer 5

so you could simplify my previous expression knowing that

Answer 6

Multiply by the conjugate of it
\[\frac{1}{8-3i} \times \frac{8+3i}{8+3i} \\ \\ \frac{8+3i}{64-9i^2} \]
We know that
\[i^2=-1\]
Can you solve it now?

Answer 7

so.. the answer would be ... 8+3i/73?

Answer 8

yes

Answer 9

Thank you :)

Answer 10

welcome :)