keiauz7
Answered

Find the product of z1 and z2, where z1 = 2(cos 80° + i sin 80°) and z2 = 9(cos 110° + i sin 110°)

Answer :

LammettHash
When multiplying complex numbers, you multiply the moduli and add the arguments:

[tex]z_1z_2=2\times9(\cos(80^\circ+110^\circ)+i\sin(80^\circ+110^\circ))=18(\cos190^\circ+i\sin190^\circ)[/tex]
kudzordzifrancis
ANSWER

[tex]z_1 z_2=18( \cos( 190 \degree ) + i \sin( 190 \degree) )[/tex]


EXPLANATION

The given complex numbers are;

[tex]z_1 = 2( \cos(80 \degree) + i \sin(80 \degree) )[/tex]

and


[tex]z_2= 9( \cos(110 \degree) + i \sin(110 \degree) )[/tex]


Recall the binominal identity for complex numbers in polar form.



[tex]z_1 z_2=r_1 r_2( \cos( \theta_1 +\theta_2) + i \sin(\theta_1 +\theta_2) )[/tex]



We apply this property to obtain,


[tex]z_1 z_2=2 \times 9( \cos( 80 \degree + 110 \degree ) + i \sin(80 \degree + 110 \degree) )[/tex]



[tex]z_1 z_2=18( \cos( 190 \degree ) + i \sin( 190 \degree) )[/tex]

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