Calculate and write in cartesian form a) \(\displaystyle{\left({2}+{i}\right)}{\left({1}-{2}{i}\right)}\) b)

Ramon Powell

Ramon Powell

Answered question

2022-03-19

Calculate and write in cartesian form
a) (2+i)(12i)
b) 3+i43i

Answer & Explanation

hinonacfp

hinonacfp

Beginner2022-03-20Added 3 answers

Step 1
a) The complex numbers in cartesian form are
z1=2+i
z2=12i
z1×z2=(2+i)(12i)
=(2)(1)+(i)(1)+(2)(2i)+(i)(2i)
=2+i4i2i2
=23i2(1)i2=1
=23i+2
=43i
Hence, (2+i)(12i)=43i
alifutlessect692

alifutlessect692

Beginner2022-03-21Added 9 answers

Step 1
b) The complex numbers in cartesian form are
z3=3+i
z4=43i
z3z4=(3+i)(43i)
Multiply numerator and denominator by (4+3i)
=(3+i)(43i)×(4+3i)(4+3i)
=(3)(4)+(i)(4)+(3)(3i)+(i)(3i)(4)2(3i)2(a+b)(ab)=a2b2
=12+4i+9i+3i2169i2
=12+13i+3(1)169(1)i2=1
=12+13i316+9
=9+13i25
=925+1325i
Hence,
(3+i)(43i)=925+1325i

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