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| 1. |
Represent in the form of a + ib.\xa0i3/2 |
| Answer» Ans.\xa0\\(let \\space (a+ib) = i^{3\\over 2}\\)Squaring Both Sides, We get\xa0\\(=> a^2 +b^2.i^2 +2abi = i^3\\)\\(=> a^2 -b^2 +2abi = -i \\space \\space \\space \\space \\space \\space \\space \\space \\space \\space [i^2 = -1]\\)On Comparing Both sides, We get\xa0\\(a^2-b^2 = 0 \\space \\space \\space \\space \\space \\space \\space and \\space \\space \\space \\space \\space \\space 2ab =-1\\)=>\xa0\\(a^2 = b^2 \\space \\space \\space ...(1) \\space \\space \\space \\space \\space and \\space \\space a = {-1\\over 2b} \\space \\space \\space \\space \\space ... (2)\\)Put value of a in (1)=>\xa0\\(({-1\\over 2b})^2 = b^2 => {1\\over 4b^2} = b^2 => {1\\over 4} = b^4 \\)=>\xa0\\(b^2 = {1\\over 2} => b = {1\\over \\sqrt 2}\\)Put value of b in (2), we get\xa0\\(a = {-1\\over 2 \\times {1\\over \\sqrt 2}} => a = {-1\\over \\sqrt2}\\)So=> \\({-1\\over \\sqrt2}+{1\\over \\sqrt 2}i = i^{3\\over 2}\\)\xa0 | |