Question

divide, answer a+bi form:
(2+8i)/(7+2i)

Answer 1

\[(\ \frac{2 + 8i}{7+2i})(\ \frac{7 - 2i}{7-2i}) = [14 - 4i + 56i - 16i ^{2}]/[49 - 4i ^{2}\]]

Answer 2

As we perform arithmetic operations note that i^2 = -1

Answer 3

Now we add like terms: \[(\ \frac{30 + 54i }{53})\]

Answer 4

Since i^2 = -1 , -16i^2 = 16
16 + 14 = 30
Also 56i - 4i = 54i (*Because they are like terms we can add them)

Answer 5

So the numerator simplifies to (30 + 52i) (*52i sorry because its (56 - 4)

Answer 6

For the denominator we have 49 - 4i^2 = 49 + 4 = 53

Answer 7

The correct final answer is therefore
\[(\ \frac{30 + 52i}{53})\]

Answer 8

Answer is \[\large \frac{2+8i}{7+2i}=\frac{30}{53}+\frac{52}{53}i\]
See attached for work shown.

Answer 9

jim did you type that yourself?