1-2 i -3 i 2-1-2 i -3 i 2 equalsA- -1B- -iC- iD- 4

The correct option is B i Let z=1+2i+3i^2/1 2i+3i^2 ⇒ z=1+2i 3/1 2i 3 ⇒ z= 2+2i/ 2 2i× 2+2i/ 2+2i ⇒ z=( 2+2i^2)/( 2)^2 (2i)^2 ⇒ z=4+4i^2 8i/4+4 ⇒ z=4 4 8i/8 ⇒ ...

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Standard XII

Mathematics

Complex Numbers

1+2 i +3 i 2/...

Question

$\frac{1 + 2 i + 3 i^{2}}{1 - 2 i + 3 i^{2}} equals$

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-1

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-i

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Solution

The correct option is C
-i

$Let z = \frac{1 + 2 i + 3 i^{2}}{1 - 2 i + 3 i^{2}} \Rightarrow z = \frac{1 + 2 i - 3}{1 - 2 i - 3} \Rightarrow z = \frac{- 2 + 2 i}{- 2 - 2 i} \times \frac{- 2 + 2 i}{- 2 + 2 i} \Rightarrow z = \frac{(- 2 + 2 i^{2})}{(- 2)^{2} - (2 i)^{2}} \Rightarrow z = \frac{4 + 4 i^{2} - 8 i}{4 + 4} \Rightarrow z = \frac{4 - 4 - 8 i}{8} \Rightarrow z = \frac{- 8 i}{8} \Rightarrow z = - i$

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Similar questions

\frac{1 + 2 i + 3 i^{2}}{1 - 2 i + 3 i^{2}}

equals
(a) i
(b) −1
(c) −i
(d) 4

Q. Complex number in the form of

A + i B

\frac{1 + 2 i + 3 i^{2}}{1 - 2 i + 3 i^{2}}

Q. Derive the following complex in the form of

A + i B

\frac{1 + 2 i + 3 i^{2}}{1 - 2 i + 3 i^{2}}

Q. Write down complex numbers in the form of

A + i B

\frac{1 + 2 i + 3 i^{2}}{1 - 2 i + 3 i^{2}}

Q. If complex number

\frac{1 + 2 i + 3 i^{2}}{1 - 2 i + 3 i^{2}}

can be written in the form of

a + i b,

then

a \cdot b =

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1+2i+3i21−2i+3i2 equals

The correct option is C -i Let z=1+2i+3i21−2i+3i2⇒ z=1+2i−31−2i−3⇒ z=−2+2i−2−2i×−2+2i−2+2i⇒ z=(−2+2i2)(−2)2−(2i)2⇒ z=4+4i2−8i4+4⇒ z=4−4−8i8⇒ z=−8i8⇒ z=−i

$\frac{1 + 2 i + 3 i^{2}}{1 - 2 i + 3 i^{2}} equals$