MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Modulus of a Complex Number

If w = z + ...

Question

If $w = \frac{z + 4 i}{z + 2 i}$ is purely imaginary then find $| z + 3 i |$

Open in App

Solution

$w = \frac{z + 4 i}{z + 2 i} L e t z = x + i y w = \frac{x + i (y + 4)}{x + i (y + 2)} O n r a t i o n a l i s i n g, = \frac{x + i (y + 4) x - i (y + 2)}{x^{2} - i^{2} {(y + 2)}^{2}} ∴ R e a l p a r t o f w \Rightarrow \frac{x^{2} + (y + 4) (y + 2)}{x^{2} + {(y + 2)}^{2}} = 0 \Rightarrow x^{2} + y^{2} + 6 y + 8 = 0 \Rightarrow x^{2} + y^{2} + 6 y + 8 + 1 = 1 T a k i n g S q u a r e r o o t o n b o t h \Rightarrow \sqrt{x^{2}} + {(y + 3)}^{2} = 1 | z + 3 i | = 1$

Suggest Corrections

thumbs-up

0

Similar questions

\frac{z + 2 i}{z - 2 i}

is purely imaginary then

| z |

z + 3 - 2 i

is purely imaginary then

\frac{z - 4}{z - 2 i}

is purely imaginary then the locus of

z

θ

z = \frac{2 + 3 i s i n θ}{1 - 2 i s i n θ}

is purely imaginary, is

z

is a complex number such that

\frac{z - i}{z - 1}

is purely imaginary, then the minimum value of

| z - (3 + 3 i) |

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Geometric Representation and Trigonometric Form

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Modulus of a Complex Number

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon