Q7 Q26.) Find the quotient of the complex numbers and leave your answer in polar form.
2 answers:
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>)
z1/z2
= 3/7 (cos(π/8-π/9) + i sin(π/8 - π/9))
= 3/7 (cos(π/72) + i sin(π/72))
<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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