# Complex number in rectangular form What is (1+2j) + (1+3j)? Your answer should contain three significant figures.

Complex number in rectangular form What is (1+2j) + (1+3j)? Your answer should contain three significant figures.
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StrycharzT
Sum of complex numbers $\left({a}_{1}+{b}_{1}i\right)+\left({a}_{2}+{b}_{2}i\right)=\left({a}_{1}+{a}_{2}\right)+\left({b}_{1}+{b}_{2}\right)i=a+bi$
$\left(1+2i\right)+\left(1+3i\right)=\left(1+1\right)+\left(2+3\right)i=2+5i$ this is the binomial form
Then find r and $\theta$
$r=\sqrt{{a}^{2}+{b}^{2}}=\sqrt{{2}^{2}+{5}^{2}}=\sqrt{29}$
if a and b are possitive then
$\theta ={\mathrm{tan}}^{-1}\left(\frac{b}{a}\right)={\mathrm{tan}}^{-1}\left(\frac{5}{2}\right)={68.2}^{\circ }$
Rectangle form
$z=r\left(\mathrm{cos}\left(\theta \right)+\mathrm{sin}\left(\theta \right)i\right)$
then $z=\sqrt{29}\left(\mathrm{cos}\left(68.2\right)+\mathrm{sin}\left(68.2\right)i\right)$
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