If zw is expressed in polar form what are r and theta ?

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1 Answer
Mar 12, 2018

#r=18" and "theta=(9pi)/8#

Explanation:

#"Given "z_1=r_1(costheta_1+isintheta_1)" and "#

#color(white)("Given ")z_2=r_2(costheta_2+isintheta_2)" then"#

#z_1z_2=r_1r_2[cos(theta_1+theta_2)+isin(theta_1+theta_2)]#

#"for "z=3(cos((3pi)/8)+isin((3pi)/8))" and "#

#color(white)("for ")w=6(cos((3pi)/4)+isin((3pi)/4))#

#rArrzw=(3xx6)[cos((3pi)/8+(3pi)/4)+isin((3pi)/8+(3pi)/4)]#

#color(white)(xxxx)=18(cos((9pi)/8)+isin((9pi)/8))#

#rArrr=18" and "theta=(9pi)/8#