Question

If z1= 1+2i and z2 =6+5i,then find |z1|/|z2|

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{\bigg|\frac{Z_{1}}{Z_{2}}\bigg|=\sqrt{\frac{3}{11}}\iota}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Z_{1} =1 + 2 \iota \\ \\ \tt: \implies Z_{2} =6 + 5 \iota \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies \bigg| \frac{ Z_{1}}{ Z_{2} } \bigg| =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Z_{1} = 1 + 2 \iota \\ \\ \tt: \implies | Z_{1}| = \sqrt{ {1}^{2} + (2 \iota) ^{2} } \\ \\ \tt: \implies | Z_{1}| = \sqrt{1 - 4} \\ \\ \tt: \implies | Z_{1}| = \sqrt{3} \iota \\ \\ \bold{Similarly : } \\ \tt: \implies Z_{2} = 6 + 5 \iota \\ \\ \tt: \implies | Z_{2}| = \sqrt{ {6}^{2} + (5\iota) ^{2} } \\ \\ \tt: \implies | Z_{2}| = \sqrt{36 - 25} \\ \\ \tt: \implies | Z_{2}| = \sqrt{11} \\ \\ \bold{For \: finding \: value : } \\ \tt: \implies \bigg| \frac{ Z_{1}}{Z_{2} } \bigg| = \frac{ \sqrt{3} \iota }{ \sqrt{11} } \\ \\ \green{\tt: \implies \bigg| \frac{ Z_{1}}{Z_{2} } \bigg| = \sqrt{ \frac{3}{11} } \iota}$

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{\bigg|\frac{Z_{1}}{Z_{2}}\bigg|=\sqrt{\frac{3}{11}}\iota}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}}$

$\tt: \implies Z_{1} =1 + 2 \iota$

$\tt: \implies Z_{2} =6 + 5 \iota$

$\red{\underline \bold{To \: Find :}}$

$\tt: \implies \bigg| \frac{ Z_{1}}{ Z_{2} } \bigg| =?$

• Given Question

$\bold{As \: we \: know \: that}$

$\tt: \implies Z_{1} = 1 + 2 \iota$

$\tt: \implies | Z_{1}| = \sqrt{ {1}^{2} + (2 \iota) ^{2} }$

$\tt: \implies | Z_{1}| = \sqrt{1 - 4}$

$\tt: \implies | Z_{1}| = \sqrt{3} \iota$

$\bold{Similarly : }$

$\tt: \implies Z_{2} = 6 + 5 \iota$

$\tt: \implies | Z_{2}| = \sqrt{ {6}^{2} + (5\iota) ^{2} }$

$\tt: \implies | Z_{2}| = \sqrt{36 - 25}$

$\tt: \implies | Z_{2}| = \sqrt{11}$

$\bold{For \: finding \: value : }$

$\tt: \implies \bigg| \frac{ Z_{1}}{Z_{2} } \bigg| = \frac{ \sqrt{3} \iota }{ \sqrt{11} }$

$\green{\tt: \implies \bigg| \frac{ Z_{1}}{Z_{2} } \bigg| = \sqrt{ \frac{3}{11} } \iota}$