Question

What is the standard form of 7 + 3i / 2 - 5i

A. -29/21 + 4/21i

B. -29/21 - 4/21i

C. 1/29 - 41/29i

D. -1/29 + 41/29i

Answer 1

Explanation:

7 + 3i / 2 - 5i would be clearer if written as (7 + 3i) / (2 - 5i). We must remove the symbol i from the denominator, and that can be accomplished by multiplying both 7 + 3i and 2 - 5i by the conjugate 2 + 5i:

(2 + 5i)(7 + 3i)

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4 + 29

which simplifies to 14 + 6i + 35i - 15 over 33, or

-1 + 41i

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33