Question

Q7. Express the complex number in the form of a +ib, if z = 3+2i
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1+i
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Answer 1

$\textsf{\large{\underline{Solution}:}}$

Given That:

$\rm: \longmapsto z = \dfrac{3 + 2i}{1 + i}$

Rationalizing the denominator, we get:

$\rm: \longmapsto z = \dfrac{(3 + 2i)(1 - i)}{(1 + i)(1 - i)}$

$\rm: \longmapsto z = \dfrac{3 - 3i + 2i + 2}{1 + 1}$

$\rm: \longmapsto z = \dfrac{5 -i}{2}$

$\rm: \longmapsto z = \dfrac{5}{2} + \dfrac{ - 1}{2} i$

Which is our required answer.

$\textsf{\large{\underline{More To Know}:}}$

$\rm1.\ i^{4n} = 1$

$\rm2. \ i^{4n+1} = i$

$\rm3.\ i^{4n+2} = -1$

$\rm4.\ i^{4n+3} = -i$

$\rm5.\ (a+bi) +(c+di) = (a + c) + (b+d)i$

$\rm6. \ (a+bi)-(c+di) = (a-c)+(b-d)i$

$\rm7.\ (a + bi)(a - bi) = a^{2}+b^{2}$

$\rm8.\ (a+bi)(c+di)= (ac-bd)+(ad+bc)i$