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Given z1 = a+bi, z2 = c+diSolve: z1 * z2 |

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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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