Question

If z1 = (3, 7) and z2 = (5, -6), then z1/z2 = ?

Answer 1

Given :-

• z₁ = (3 , 7)
• z₂ = (5 , -6)

that is,

$\bullet \: \: \sf{z_1 = 3 + 7i}$

$\bullet \: \: \sf{z_2 = 5 - 6i}$

To find :-

$\bullet \: \: \sf{ \dfrac{z_1}{z_2} }$

Solution :-

$\implies \sf{ \dfrac{z_1}{z_2} }$

putting values of z₁ and z₂

$\implies \sf{ \dfrac{3 + 7i}{5 - 6i} }$

mutiplying and dividing by 5 + 6 i

$\implies \sf{ \dfrac{3 + 7i}{5 - 6i} \times \dfrac{5 + 6i}{5 + 6i} }$

$\implies \sf{ \dfrac{15 + 18i + 35i + 42 \: {i}^{2} }{( {5})^{2} - ({6i})^{2} }}$

$\implies \sf{ \dfrac{15 + 53i + 42 \: {i}^{2} }{ 25 - 36 \: {i}^{2} }}$

putting i² = -1

$\implies \sf{ \dfrac{15 + 53i + 42 \: ( - 1)}{ 25 - 36 \: ( - 1) }}$

$\implies \sf{ \dfrac{15 + 53i - 42 }{ 25 + 36 }}$

$\implies \sf{ \dfrac{ - 27 + 53i }{ 61 }}$

$\implies \sf{ \dfrac{ - 27}{61} + \dfrac{ 53i }{ 61 }}$

therefore,

$\boxed{ \boxed{ \red{ \sf{ \frac{z_1}{z_2} = \frac{ - 27}{61} + \frac{53}{61} i}}}}$