If z -1-1- i 2-3 i - - then - z -A- 1B- 1-26C- 5-26D- none of these

The correct option is B 1/√(26) Let z=1/(1 i)(2+3i) ⇒ z=1/2+i 3i^2 ⇒ z=1/2+i+3 ⇒ z=1/5+i×5 i/5 i ⇒ z=5 i/25 i^2 ⇒ z=5 i/25+1 ⇒ z=5 i/26 ⇒ z=5/26 i/26 ⇒ |z|=√ ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Complex Numbers

If z =1/1- i ...

Question

If $z = \frac{1}{(1 - i) (2 + 3 i)},$ , then |z| =

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$\frac{1}{\sqrt{26}}$

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$\frac{5}{\sqrt{26}}$

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none of these

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Solution

The correct option is B
$\frac{1}{\sqrt{26}}$

$Let z = \frac{1}{(1 - i) (2 + 3 i)} \Rightarrow z = \frac{1}{2 + i - 3 i^{2}} \Rightarrow z = \frac{1}{2 + i + 3} \Rightarrow z = \frac{1}{5 + i} \times \frac{5 - i}{5 - i} \Rightarrow z = \frac{5 - i}{25 - i^{2}} \Rightarrow z = \frac{5 - i}{25 + 1} \Rightarrow z = \frac{5 - i}{26} \Rightarrow z = \frac{5}{26} - \frac{i}{26} \Rightarrow | z | = \sqrt{\frac{25}{676} + \frac{1}{676}} \Rightarrow z = \frac{1}{\sqrt{26}}$

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Similar questions

If z = \frac{1}{(1 - i) (2 + 3 i)}, than |z| =

(a) 1
(b)

1 / \sqrt{26}

(c)

5 / \sqrt{26}

(d) none of these

Q. If

z = \frac{1}{(1 - i) (2 + 3 i)}

, then

| z | =

Q. If

z = \frac{1 + 2 i}{1 - (1 - i)^{2}}

, then arg (z) equal
(a) 0
(b)

\frac{π}{2}

If $z = \frac{1 + 2 i}{1 - (1 - i)^{2}}$ , then arg (z) equals

If $z = \frac{1}{(2 + 3 i)^{2}}$ , then |z| =

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If z=1(1−i)(2+3i),, then |z| =

The correct option is B 1√26 Let z=1(1−i)(2+3i)⇒ z=12+i−3i2⇒ z=12+i+3⇒ z=15+i×5−i5−i⇒ z=5−i25−i2 ⇒ z=5−i25+1⇒ z=5−i26 ⇒ z=526−i26⇒ |z|=√25676+1676⇒ z=1√26

If $z = \frac{1}{(1 - i) (2 + 3 i)},$ , then |z| =