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

vestirme4
2021-05-29
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StrycharzT

Answered 2021-05-30
Author has **102** answers

Sum of complex numbers $({a}_{1}+{b}_{1}i)+({a}_{2}+{b}_{2}i)=({a}_{1}+{a}_{2})+({b}_{1}+{b}_{2})i=a+bi$

$(1+2i)+(1+3i)=(1+1)+(2+3)i=2+5i$ 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

$\theta ={\mathrm{tan}}^{-1}(\frac{b}{a})={\mathrm{tan}}^{-1}(\frac{5}{2})={68.2}^{\circ}$

Rectangle form

$z=r(\mathrm{cos}(\theta )+\mathrm{sin}(\theta )i)$

then$z=\sqrt{29}(\mathrm{cos}(68.2)+\mathrm{sin}(68.2)i)$

Then find r and

if a and b are possitive then

Rectangle form

then

Jeffrey Jordon

Answered 2022-01-30
Author has **2027** answers

Answer is given below (on video)

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