Which of the following is equivalent to 5+i/1+3i

Question

A. 4-8i/5

B. 4-7i/5

C. 1-7i/5

D. -1-7i/4

Answer 1

Recall that y/z = y*conj(z) / |z|².

You get

(5 + i) / (1 + 3i) = (5 + i)(1 - 3i) / |1 + 3i|²

= (5*1 + i*(-3i) + 5*(-3i) + i*1) / (1² + 3²)

= (5 + 3 - 15i + i) / 10

= (8 - 14i) / 10

= (4 - 7i) / 5

Answer 2

(5+i)/(1+3i)

= (5+i)(1-3i)/(1+3^2), multipying the top and the bottom by 1-3i, the conjugate of 1+3i.

= (5+3 + i - 15i)/(10)

= (4-7i)/5

Answer: B

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