Find the Quotient of the complex number: 6/7-2i?

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Find the Quotient of the complex number: 6/7-2i?

2006-07-28 05:33:01 · 2 answers · asked by Brandon ツ 3 in Science & Mathematics ➔ Mathematics

2 answers

Multiply both sides of the fraction by the conjugate of the denominator

Top: 6(7+2i)

Bottom: (7-2i)(7+2i)

FOIL on bottom: you get 49 - 4i^2 = 49+4 = 53

Distribute on top

Final answer: (42+12i)/53

2006-07-28 05:50:05 · answer #1 · answered by jenh42002 7 · 3⤊ 1⤋

6 / (7 - 2i)

You start by multiplying both the numerator and denominator (to keep it balanced) by the conjugate of "7 - 2i" which is "7 + 2i"

[6 * (7 + 2i) ] / [ (7 - 2i) * (7 + 2i) ]
= (42 + 12i) / (49 - 14i + 14i + 4)
=(42 + 12i) / 53
=(42/53) + (12i/53)

2006-07-28 10:47:16 · answer #2 · answered by Anonymous · 0⤊ 0⤋