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Answer:

You need to remember two complex numbers multiplication such that:

`z_1*z_2 = (a+bi)(c+di)`

You need to multiply each term from a+bi by the brackets `(c+di)` such that:

`z_1*z_2 = a*(c+di) + bi*(c+di)`

You need to open brackets such that:

`z_1*z_2 = ac + adi + bci + bdi^2`

You need to use `i^2 = -1` such that:

`z_1*z_2 = ac + adi + bci - bd`

You need to collect real parts and imaginary parts such that:

`z_1*z_2 = (ac-bd) + (adi + bci)`

You need to factor out i such that:

`z_1*z_2 = (ac-bd) + i(ad + bc)`

**Hence, multiplying the complex numbers `z_1` and `z_2` yields the complex number `z = (ac-bd) + i(ad + bc).` **

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