Question

The conjugate of ( -2 + 3 i ) ( 5 – i ) is
(a) ( -2 + 3 i ) ( 5 + i ) (b) ( -2 – 3 i )( 5 – i ) (c) - 7 - 17 i (d) -13 + 17 i

Answer 1

Answer:

(-2-3i)(5-i)

Step-by-step explanation:

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Answer 2

Given,

A complex number ( -2 + 3i )( 5 – 1i ).

To find,

The conjugate of the given complex number.

Solution,

• We can simply find the conjugate of a complex number by changing the sign of the imaginary part.

• The conjugate of a complex number (a + ib) would be (a - ib).

Now,

• First, we will multiply the complex number ( -2 + 3i )( 5 – 1i ).

        ⇒ -2( 5 - 1i ) + 3i( 5 - 1i ) =( -2 )( 5 ) + ( -2 )( -1i ) + ( 3i )( 5 ) + ( 3i )( -1i )

        ⇒ -10 + 2i + 15i - 3i²

        ⇒ -10 + 2i +15i -3(-1)      (Note: i² = -1, where, i is an imaginary number.)

        ⇒ -10 + 17 i +3 = - 7 + 17i.

• After multiplying the complex numbers we get the product as = -7 + 17i

• The conjugate of - 7 + 17i  will be -7 - 17i.

Hence, The conjugate of ( -2 + 3 i ) ( 5 – i ) is -7 - 17i. (Option c)