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Question

Express (2+3i)3 in the form (a+ib)

A
46+9i
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B
40+7i
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C
469i
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D
46+9i
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Solution

The correct option is A 46+9i
We know that
(z1+z2)3=z31+z32+3z1z2(z1+z2).
(2+3i)3=23+(3i)3+3×2×3i(2+3i)
=8+27i3+36i+54i2
=827i+36i54 [ i3=i,i2=1]
=46+9i

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