Question

Given that x = 4 + 3i and y = 2 + 5i, match the expressions to their answers.

Answer 1

Hence the correct answers are:

• 2x-y = 6+i
• -4x.2y=56-208i
• 3x+5y=22+34i
• x.4y=-28+104i

Further explanation:

When operators are applied on complex numbers, the real part is combined with real numbers and the imaginary part is calculated with imaginary part.

$Given\\x=4+3i\\y=2+5i$

1. 2x-y

$2x-y = 2(4+3i)-(2+5i)\\= 8+6i-2-5i\\=6+i$

2. -4x.2y

$4x.2y = -4(4+3i) * 2(2+5i)\\= (-16-12i)*(4+10i)\\=-16(4+10i)-12i(4+10i)\\=-64-160i-48i-120(i*i)\\=-64-208i-120(-1)\\=-64-208i+120\\=56-208i$

3. 3x+5y

$3x+5y = 3(4+3i)+5(2+5i)\\= 12+9i+10+25i\\=22+34i$

4. x.4y

$x.4y=(4+3i)* 4(2+5i)\\= (4+3i)(8+20i)\\=4(8+20i)+3i(8+20i)\\=32+80i+24i+60(i*i)\\=32+104i+60(-1)\\=32+104i-60\\=-28+104i$

Hence the correct answers are:

• 2x-y = 6+i
• -4x.2y=56-208i
• 3x+5y=22+34i
• x.4y=-28+104i

Keywords: Complex numbers, Operations on complex numbers

Learn more about complex numbers at:

• brainly.com/question/1021953
• brainly.com/question/10250188

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