Question

pls answer complex numbers chapter
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Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{\dfrac{\sqrt{3}-i\sqrt{2}}{\sqrt{3}+i\sqrt{2}}+\dfrac{-\sqrt{12}+i\sqrt{8}}{\sqrt{3}+i\sqrt{2}}}$

$\tt{=\dfrac{\sqrt{3}-i\sqrt{2}}{\sqrt{3}+i\sqrt{2}}+\dfrac{-\sqrt{4\times3}+i\sqrt{4\times2}}{\sqrt{3}+i\sqrt{2}}}$

$\tt{=\dfrac{\sqrt{3}-i\sqrt{2}}{\sqrt{3}+i\sqrt{2}}+\dfrac{-2\sqrt{3}+2i\sqrt{2}}{\sqrt{3}+i\sqrt{2}}}$

$\tt{=\dfrac{\sqrt{3}-i\sqrt{2}}{\sqrt{3}+i\sqrt{2}}+\dfrac{-2(\sqrt{3}-i\sqrt{2})}{\sqrt{3}+i\sqrt{2}}}$

$\tt{=\bigg\{\dfrac{\sqrt{3}-i\sqrt{2}}{\sqrt{3}+i\sqrt{2}}\bigg\}-2\bigg\{\dfrac{\sqrt{3}-i\sqrt{2}}{\sqrt{3}+i\sqrt{2}}\bigg\}}$

$\tt{=-\dfrac{(\sqrt{3}-i\sqrt{2})(\sqrt{3}-i\sqrt{2})}{(\sqrt{3}+i\sqrt{2})(\sqrt{3}-i\sqrt{2})}}$

$\tt{=-\dfrac{(\sqrt{3}-i\sqrt{2})^2}{(\sqrt{3})^2+(\sqrt{2})^2}}$

$\tt{=-\dfrac{(\sqrt{3})^2+(i\sqrt{2})^2-2\cdot\sqrt{3}\cdot(i\sqrt{2})}{(\sqrt{3})^2+(\sqrt{2})^2}}$

$\tt{=-\dfrac{3-2-(2\sqrt{6})i}{3+2}}$

$\tt{=-\dfrac{1-(2\sqrt{6})i}{5}}$

$\tt{=-\dfrac{1}{5}+\dfrac{2\sqrt{6}}{5}i}$

Answer 2

Answer:

√3-i√2)/(√3+i√2) -2{√3-i√2)/{(√3+I√2)

=-{√3-i√2)/(√3+i√2)

={(√3-i√2)^2/{(√3+i√2)(√3-i√2)}

=√3-i√2)^2/(3+2)

=(3+2-2√6i)/5

=(5/5)-(2√6/5)I

=1-(2√6/5)i