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What is the product of the complex numbers 3-4i3−4i3, minus, 4, i and -6+i−6+iminus, 6, plus, i, where i=\sqrt{-1}i= −1 ​ i, equals, square root of, minus, 1, end square root ?

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lublana

Answer:

[tex]z_1\times z_2=-14+27i[/tex]

Step-by-step explanation:

We are given that two complex numbers

[tex]z_1=3-4i[/tex]

[tex]z_2=-6+i[/tex]

We have to find the product of two complex numbers

[tex]z_1\times z_2=(3-4i)(-6+i)[/tex]

[tex]z_1\times z_2=3(-6+i)-4i(-6+i)[/tex]

[tex]z_1\times z_2=-18+3i+24i-4i^2[/tex]

[tex]z_1\times z_2=-18+27i+4[/tex] ([tex]i^2=-1[/tex])

[tex]z_1\times z_2=-14+27i[/tex]

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