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Question

Express the following in the form a +bi, where a and b are real numbers.

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Solution

1+i1i=1+i1i×1+i1+i=(1+i)212i2=1+2i+i21+1=1+2i12=i=0+1i.(ii)(1i1+i)2=12i+i21+2i+i2=12i11+2i1=2i2i=1=1+0i.(iii)(1+i1i)=[1+i1i×1+i1+i]=(1+i)21i2=1+i2+2i1(1)=11+2i2=i(1+i1i)3=i3=i.i2=i=01i.[Using(i)]
(iv)(3+5i)(35i)(3+2i)(32i)=95i222i=9+522i=1422i=1422iii=14i22i2=722i.

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