Division of Complex Numbers

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Division of Complex Numbers

Complex Numbers, Division of Complex Numbers - IB Mathematics HL

How can we find $\frac{z}{w}$

given that

$z=3+4i$ and $w=5-2i$

Thanks
lora

Posts: 0
Joined: Wed Apr 10, 2013 7:36 pm

Re: Division of Complex Numbers

When dividing two complex numbers, we multiply the numerator and denominator by the conjugate of the denominator such as the product in the denominator to become a real number.

$\frac{z}{w}= \frac{a+ib}{c+di}= \frac{a+ib}{c+di} \cdot \frac{c-di}{c-di}$

$}= \frac{(a+ib)(c-di)}{(c^2-(di)^2)}$

$}= \frac{(ac-adi+bci+bd)}{(c^2+d^2)}$

$}= \frac{(ac+bd)+(bc-ad)i)}{(c^2+d^2)}$

Thus about your question we have that

$}= \frac{(3+4i)(5+2i)}{(5^2-(2i)^2)}$

$}= \frac{(7+26i)}{29}$

$}= \frac{7}{29} + \frac{26}{29} \cdot i$
lily

Posts: 0
Joined: Mon Jan 28, 2013 8:04 pm

Re: Division of Complex Numbers

Thanks Lily!!
lora

Posts: 0
Joined: Wed Apr 10, 2013 7:36 pm

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