The expressions which are equivalent to the complex number 45 + 2i are (9 + 4i) + (36 - 2i) and (9 + 4i) + 2(4 + 7i)(1 - 2i).
1) (2 + 8i) + (30 – 6i) which gives 32 + 2i.
Hence not equivalent.
2) (13 + 4i) + (32 – 61) which is equal to the 45 - 2i.
So, not equivalent.
3) (9 + 4i) + (36 - 2i) which gives 45 + 2i.
Therefore, the expression (9 + 4i) + (36 - 2i) is equivalent to the 45 + 2i.
4) (2+ 8i) + 2(9 + 6i)(1- i) which on solving gives 32 + 2i.
Hence this expression is not equivalent.
5) (13 + 4i) + 2(7 + 2i)(2-i) which gives 45 - 2i.
Hence not equivalent.
6) (9 + 4i) + 2(4 + 7i)(1 - 2i) which gives 45 + 2i.
Hence this expression is equivalent.
Expressions (9 + 4i) + (36 - 2i) and (9 + 4i) + 2(4 + 7i)(1 - 2i) are equivalent to 45 + 2i.
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