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n200080 [17]
3 years ago
9

Q7 Q26.) Find the quotient of the complex numbers and leave your answer in polar form.

Mathematics
2 answers:
irina [24]3 years ago
8 0

To divide complex numbers in polar form, divide the r parts and subtract the angle parts. Or


<span><span><span><span>r2​</span><span>(<span>cos<span>θ2​ </span>+ i</span> sin<span>θ2​</span>) / </span></span><span><span>r1​</span><span>(<span>cos<span>θ1 </span>+ i</span> sin<span>θ1​</span>)</span></span></span>​</span> <span>= <span><span><span>r2/​</span><span>r1​</span></span>​</span><span>(cos(<span><span>θ2</span>−<span>θ1​) </span></span>+ i sin(<span><span>θ2​</span>−θ1)</span><span>)
</span></span></span>

z1/z2

= 3/7 (cos(π/8-π/9) + i sin(π/8 - π/9))

= 3/7 (cos(π/72) + i sin(π/72))


Taya2010 [7]3 years ago
4 0

<span><span><span>r1​<span>(<span>cosθ1​ + i</span> sinθ1​) / </span></span><span>r2<span>(<span>cosθ2 + i</span> sinθ2​)</span></span></span>​</span> <span>= <span><span>r1/​r2​</span>​</span><span>(cos(<span>θ1−θ2​) </span>+ i sin(<span>θ1​−θ2)</span><span>)</span></span></span>

<span><span><span>z1/z2</span></span></span>

<span><span><span>=3(cos(pi/8)+isin(pi/8)/7(cos(pi/9)+isin(pi/9)</span></span></span>

<span><span><span>=3/7(cos(pi/8-pi/9)+isin(pi/8-pi/9)</span></span></span>

<span><span><span>=3/7(cos(pi/72)+isin(pi/72)</span></span></span>

<span><span><span /></span></span>

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