write the complex number in standard form 32i232i 5iSolutio

write the complex number in standard form: (3-2i)^2(3+2i)
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(5-i)

Solution

(3-2i)^2(3+2i) = (3-2i)(9+4) = 13(3-2i), since (3-2i)(3+2i) = 9+4
1/(5-i) = (5+i)/26
So,

(3-2i)^2(3+2i)/(5-i)
= 13(3-2i)(5+i)/26
= (1/2)(15+2 +3i-10i)
= (17/2) - (7/2)i