Question

If Z1 = a + ib and Z2 = c + id are two complex numbers then the product
Z1 Z2 is defined as​

Answer 1

If z1 = a + ib and z2 = c + id are complex numbers such that |z1| = |z2| = 1 and Re(z1 z2) = 0 , then the pair of complex numbers w1 = a + ic and w2 = b + id satisfy.

Step-by-step explanation:

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Answer 2

Given,

$\[\begin{array}{l}{z_1} = a + ib\\{z_2} = c + id\end{array}\]$

Solution,

$\[\begin{array}{l} = |{z_1}{z_2}|\\ = \left( {a + ib} \right)\left( {c + id} \right)\\ = ac + iad + ibc + {i^2}bd\end{array}\]$

Know that, $\[{i^2} = - 1\]$.

$\[ = ac + iad + ibc - bd\]$

$\[ = ac - bd + i\left( {ad + bc} \right)\]$

Real part $\[ = ac - bd\]$

Imaginary part $\[ = \left( {ad + bc} \right)\]$