Math, asked by issacbharti5953, 1 year ago

If z1= 2+3i,z2=1+2i then find z1/z2

Answers

Answered by mad210203
12

Given:

Two complex numbers:  \[{{z}_{1}}=2+3i\]\\ and \[{{z}_{1}}=1+2i\].

To find:

We need to find the value of  \frac{z_1}{z_2}.

Solution:

\[\Rightarrow \frac{{{z}_{1}}}{{{z}_{2}}}=\frac{2+3i}{1+2i}\]

Now, rationalize the denominator.

\[\Rightarrow \frac{{{z}_{1}}}{{{z}_{2}}}=\frac{2+3i}{1+2i}\times \frac{1-2i}{1-2i}\]

Multiply the terms in numerator and denominator.

\Rightarrow \frac{{{z}_{1}}}{{{z}_{2}}}=\frac{\left( 2+3i \right)\left( 1-2i \right)}{\left( 1+2i \right)\left( 1-2i \right)}

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

\Rightarrow \frac{{{z}_{1}}}{{{z}_{2}}}=\frac{2-4i+3i-6{{i}^{2}}}{1-2i+2i-4{{i}^{2}}}

The value of i^2 is equal to -1.

& \Rightarrow \frac{{{z}_{1}}}{{{z}_{2}}}=\frac{2-4i+3i-6(-1)}{1-2i+2i-4(-1)}

\Rightarrow \frac{{{z}_{1}}}{{{z}_{2}}}=\frac{2-4i+3i+6}{1-2i+2i+4}

\Rightarrow \frac{{{z}_{1}}}{{{z}_{2}}}=\frac{8-i}{5}

\Rightarrow \frac{{{z}_{1}}}{{{z}_{2}}}=\frac{8}{5}-\frac{i}{5}

Therefore, the value of \frac{{{z}_{1}}}{{{z}_{2}}} is \frac{8}{5}-\frac{i}{5}.

Answered by vishalshinde8046
1

Answer:

. find answer...........

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