If z-2-3- find Rez- Imz- z- and -z-

The given number may be written as z=(√(2) i √(3)). ∴ Re(z)=√(2), Im(z)= √(3), z̅=(̅√̅(̅2̅)̅ ̅i̅√̅(̅3̅)̅)̅ =(√(2)+i√(3)) and |z|^2 =[(√(2))^2+( √(3))^2]=(2+ ...

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Byju's Answer

Standard XI

Mathematics

Factorization Method Form to Remove Indeterminate Form

If z=√2-√-3, ...

Question

If $z = (\sqrt{2} - \sqrt{- 3})$ , find Re(z), Im(z), $¯ z$ and |z|.

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Solution

The given number may be written as

$z = (\sqrt{2} - i \sqrt{3})$ .

$∴ R e (z) = \sqrt{2}, I m (z) = - \sqrt{3}, ¯ z = ¯ (\sqrt{2} - i \sqrt{3}) = (\sqrt{2} + i \sqrt{3})$

and $| z |^{2} = [(\sqrt{2})^{2} + (- \sqrt{3})^{2}] = (2 + 3) = 5 \Rightarrow | z | = \sqrt{5}$

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Similar questions

Q. If

z = (\sqrt{3} + i)

then find Re(z) and Im(z).

Q. If

∣ z - i R e (z) ∣=∣ z - I m (z) ∣,

then z lies on

Q. If

z

and

w

be two complex numbers such that

| z | \leq 1, | w | \leq 1

and

| z + i w | = | z - i ¯ ¯¯ ¯ w | = 2,

then

Q. If

z

is a complex number satisfying

z + ¯ ¯ ¯ z = 0

, then

Q. If

z = {(\frac{\sqrt{3}}{2} + \frac{i}{2})}^{5} + {(\frac{\sqrt{3}}{2} - \frac{i}{2})}^{5},

then
(a) Re (z) = 0
(b) Im (z) = 0
(c) Re (z) > 0, Im (z) > 0
(d) Re (z) > 0, Im (z) < 0

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If z=(√2−√−3), find Re(z), Im(z), ¯z and |z|.

The given number may be written as z=(√2−i√3). ∴Re(z)=√2, Im(z)=−√3, ¯z=¯(√2−i√3)=(√2+i√3) and |z|2=[(√2)2+(−√3)2]=(2+3)=5⇒|z|=√5

If $z = (\sqrt{2} - \sqrt{- 3})$ , find Re(z), Im(z), $¯ z$ and |z|.

The given number may be written as

$z = (\sqrt{2} - i \sqrt{3})$ .

$∴ R e (z) = \sqrt{2}, I m (z) = - \sqrt{3}, ¯ z = ¯ (\sqrt{2} - i \sqrt{3}) = (\sqrt{2} + i \sqrt{3})$

and $| z |^{2} = [(\sqrt{2})^{2} + (- \sqrt{3})^{2}] = (2 + 3) = 5 \Rightarrow | z | = \sqrt{5}$