If 1-i2-3i3-4i 2-3i1-i3-4i -a-ib- then a 2 - b 2 -

The correct option is E 1 Given, (1+i)(2+3i)(3 4i) (2 3i)(1 i)(3+4i) =a+ib , then a ^ 2 + b ^ 2 ⇒| (1+i)(2+3i)(3 4i) (2 3i)(1 i)(3+4i) ...

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Byju's Answer

Standard XII

Mathematics

Modulus of a Complex Number

If 1+i2+3i3...

Question

If $\frac{(1 + i) (2 + 3 i) (3 - 4 i)}{(2 - 3 i) (1 - i) (3 + 4 i)} = a + i b$ , then $a^{2} + b^{2} =$

132

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Solution

The correct option is E $1$
Given, $\frac{(1 + i) (2 + 3 i) (3 - 4 i)}{(2 - 3 i) (1 - i) (3 + 4 i)} = a + i b$ , then $a^{2} + b^{2}$
$\Rightarrow ∣ ∣ ∣ \frac{(1 + i) (2 + 3 i) (3 - 4 i)}{(2 - 3 i) (1 - i) (3 + 4 i)} ∣ ∣ ∣ = | a + i b |$
$\Rightarrow \frac{\sqrt{1 + 1} \sqrt{4 + 9} \sqrt{9 + 16}}{\sqrt{4 + 9} \sqrt{1 + 1} \sqrt{9 + 16}} = \sqrt{a^{2} + b^{2}}$
Squaring both sides we get
$\frac{2 \times 13 \times 25}{13 \times 2 \times 25} = a^{2} + b^{2}$
$∴ a^{2} + b^{2} = 1$

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If (1+i)(2+3i)(3−4i)(2−3i)(1−i)(3+4i)=a+ib, then a2+b2=

The correct option is E 1Given, (1+i)(2+3i)(3−4i)(2−3i)(1−i)(3+4i)=a+ib, then a2+b2⇒∣∣∣(1+i)(2+3i)(3−4i)(2−3i)(1−i)(3+4i)∣∣∣=|a+ib|⇒√1+1√4+9√9+16√4+9√1+1√9+16=√a2+b2Squaring both sides we get2×13×2513×2×25=a2+b2∴a2+b2=1

If $\frac{(1 + i) (2 + 3 i) (3 - 4 i)}{(2 - 3 i) (1 - i) (3 + 4 i)} = a + i b$ , then $a^{2} + b^{2} =$